Krzysztof Burdzy

Multiplicative functional for reflected Brownian motion via deterministic (2009)

Abstract. We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear map...

Krzysztof Burdzy, M. Lee

Abstract. We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the...

Pathwise uniqueness for a degenerate stochastic differential equation (2009)

F. Bass, Krzysztof Burdzy, Zhen-qing Chen

We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation dXt =|Xt | α dWt, where Wt is a one-dimensional Brownian motion and α...

Stationary distributions for diffusions with inert drift (forthcoming paper (2009)

Richard F. Bass, Krzysztof Burdzy, Zhen-qing Chen, Martin Hairer

Consider a reflecting diffusion in a domain in R d that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the...

PROBABILITY IS SYMMETRY On Foundations of the Science of Probability (2008)

ON THE ROBIN PROBLEM IN FRACTAL DOMAINS (2008)

Richard F. Bass, Krzysztof Burdzy, Zhen-qing Chen

Abstract. We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum is greater than 0, and some other...

Markov processes with product-form stationary distribution (2008)

Burdzy, Krzysztof; University Of Washington; Burdzy@math.washington.edu, White, David; Belmont University; White@u.washington.edu

We consider a continuous time Markov process (X,L), where X jumps between a finite number of states and L is a piecewise linear process with state space Rd. The process L represents an “inert...

The Skorokhod problem in a time-dependent interval (2008)

Krzysztof Burdzy, Weining Kang, Kavita Ramanan

Abstract: We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving...

Differentiability of stochastic flow of reflected Brownian motions (2008)

Multiplicative functional for reflected Brownian motion via deterministic ODE (2008)

We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear map represented by...

Burdzy, Krzysztof, Lee, John M.

We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the...

Stationary distributions for diffusions with inert drift (2008)

Bass, Richard F., Burdzy, Krzysztof, Chen, Zhen-Qing, Hairer, Martin

Consider a reflecting diffusion in a domain in $R^d$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for...

A change of variable formula with It\^o correction term (2008)

Burdzy, Krzysztof, Swanson, Jason

We consider the solution u(x,t) to a stochastic heat equation. For fixed x, the process F(t)=u(x,t) has a nontrivial quartic variation. It follows that F is not a semimartingale, so a stochastic...

ON THE ROBIN PROBLEM IN FRACTAL DOMAINS (2008)

Richard F. Bass, Krzysztof Burdzy, Zhen-qing Chen

Abstract. We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum of the solution to the mixed...

On the "Hot Spots" Conjecture of J. Rauch (2008)

Rodrigo Bañuelos, Krzysztof Burdzy

this paper, we consider the solutions of the heat equation relative to the "one-half Laplacian" operator, (1=2)\Delta, which is a convenient normalization for arguments involving Brownian...

Contents (2008)

Krzysztof Burdzy, Jason Swanson

We consider the solution u(x, t) to a stochastic heat equation. For fixed x, the process F (t) = u(x, t) has a nontrivial quartic variation. It follows that F is not a semimartingale, so a stochastic...

On the Robin problem in fractal domains (2008)

Bass, Richard F., Burdzy, Krzysztof, Chen, Zhen-Qing

We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum of the solution to the mixed...

The Skorokhod problem in a time-dependent interval (2007)

Burdzy, Krzysztof, Kang, Weining, Ramanan, Kavita

We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving boundaries may...

Efficient Markovian couplings: examples and (2007)

Krzysztof Burdzy, Wilfrid S. Kendall

by

ON THE “HOT SPOTS ” CONJECTURE OF J. RAUCH (2007)

Rodrigo Bañuelos, Krzysztof Burdzy

d ≥ 1. Let u(t, x),t ≥ 0,x ∈ D, be the solution of the heat equation ∂u/∂t = (1/2)∆xu in D with the Neumann boundary conditions and the initial condition u(0,x)=u0(x). That is, u(t, x) is...

SUPER-BROWNIAN MOTION WITH REFLECTING HISTORICAL PATHS (2007)

Uperieure S Ormale, N Ecole, K. Burdzy, K. Burdzy, Krzysztof Burdzy, ...

Super-Brownian motion with

is the standard Brownian motion with (2007)

And Consider The, Martin Barlow, Krzysztof Burdzy, Haya Kaspi, Avi Mandelbaum

ns of (1) with the same # # [-1, 1] \ {0}, relative to the same Brownian motion B t , then X x t = X y t for some t < #, a.s. Proof. For simplicity assume that # > 0 and 0 = x < y. Let b L 0...

THE SUPREMUM OF BROWNIAN LOCAL TIMES ON Hölder Curves (2007)

Super-Brownian Motion With Reflecting Historical Paths (2007)

. For f : [0; 1] ! R, we consider L f t , the local time of space-time Brownian motion on the curve f . Let S be the class of all functions whose Holder norm of order is less than or equal to 1. We...

Non-Increase Of Brownian Motion Via Branching Process Argument (2007)

. We consider super-Brownian motion whose historical paths reect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions...

COALESCENCE OF SYNCHRONOUS COUPLINGS (2007)

. A new proof of the non-increase of Brownian paths is given. 1. Introduction. We will give a new proof of the classical result on non-increase of Brownian paths and present a short review of other...

Polish Academy of Sciences and Wroc law University of Technology (2007)

re ected inside a planar domain D, i.e., a vector process (X t; Y t) such that X t and Y t are re ected Brownian motions in D, and for every (random) interval (t 1; t 2) such that neither

Krzysztof Burdzy, Tadeusz Kulczycki

Abstract. Let X(t) be the symmetric -stable process in R d

Markov processes with product-form stationary distribution (2007)

Burdzy, Krzysztof, White, David

We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for...

On pathwise uniqueness for reflecting Brownian motion in $C^{1+\gamma}$ domains (2007)

Markov processes with product-form stationary distribution (2007)

Pathwise uniqueness holds for the Skorokhod stochastic differential equation in $C^{1+\gamma}$ domains in $\mathbb{R}^d$ for $\gamma >1/2$ and $d\geq3$.

Krzysztof Burdzy, David White

This research has been inspired by several papers on processes with inert drift [5, 6, 4, 3, 1]. The model involves a “particle ” X and an “inert drift ” L, neither of which is a Markov...

On pathwise uniqueness for reflecting Brownian motion in C 1+γ domains ∗ (2007)

Discrete Approximations to Reflected Brownian Motion ∗ (2007)

Pathwise uniqueness holds for the Skorokhod stochastic differential equation in C 1+γ-domains in R d for γ> 1/2 and d ≥ 3.

Discrete approximations to reflected Brownian motion (2006)

In this paper we investigate three discrete or semi-discrete approximation schemes for reflected Brownian motion on bounded Euclidean domains. For a class of bounded domains D in R n that includes...

Burdzy, Krzysztof, Chen, Zhen-Qing

In this paper we investigate three discrete or semi-discrete approximation schemes for reflected Brownian motion on bounded Euclidean domains. For a class of bounded domains $D$ in $\mathbb{R}^n$...

An annihilating–branching particle model for the heat equation with average temperature zero (2006)

Burdzy, Krzysztof, Quastel, Jeremy

We consider two species of particles performing random walks in a domain in ℝd with reflecting boundary conditions, which annihilate on contact. In addition, there is a conservation law so that the...

Pathwise uniqueness for reflecting Brownian motion in certain planar Lipschitz domains (2006)

Bass, Richard F.; University Of Connecticut; Bass@math.uconn.edu, Burdzy, Krzysztof; University Of Washington; Burdzy@math.washington.edu

We give a simple proof that in a Lipschitz domain in two dimensions with Lipschitz constant one, there is pathwise uniqueness for the Skorokhod equation governing reflecting Brownian motion.

Mirror couplings and Neumann eigenfunctions (2006)

Atar, Rami, Burdzy, Krzysztof

We analyze a pair of reflected Brownian motions in a planar domain $D$, for which the increments of both processes form mirror images of each other when the processes are not on the boundary. We show...

Pathwise uniqueness for a degenerate stochastic differential equation (2006)

Bass, Richard F., Burdzy, Krzysztof, Chen, Zhen-Qing

We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation \[dX_t=|X_t|^{\alpha} dW_t,\] where $W_t$ is a one-dimensional Brownian...

MIRROR COUPLINGS AND NEUMANN EIGENFUNCTIONS (2006)

Rami Atar, Krzysztof Burdzy

We analyze a pair of reflected Brownian motions in a planar domain D, for which the increments of both processes form mirror images of each other when the processes are not on the boundary. We show...

Pathwise uniqueness for two dimensional reflecting Brownian motion in Lipschitz domains (2005)

Benjamini, Itai, Burdzy, Krzysztof, Chen, Zhen-Qing

We give a simple proof that in a Lipschitz domain in two dimensions with Lipschitz constant one, there is pathwise uniqueness for the Skorokhod equation governing reflecting Brownian motion.

Shy couplings (2005)

A pair of Markov processes is called a Markov coupling if both processes have the same transition probabilities and the pair is also a Markov process. We say that a coupling is ``shy'' if the...

The hot spots problem in planar domains with one hole (2005)

On the Robin problem in fractal domains (2005)

There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside...

Bass, Richard, Burdzy, Krzysztof, Chen, Zhen-Qing

We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum of the solution is greater than 0, and some...

Lenses in Skew Brownian Flow (2005)

Burdzy, Krzysztof, Kaspi, Haya

We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the...

An annihilating--branching particle model for the heat equation with average temperature zero (2005)

Burdzy, Krzysztof, Quastel, Jeremy

We consider two species of particles performing random walks in a domain in $\mathbb{R}^d$ with reflecting boundary conditions, which annihilate on contact. In addition, there is a conservation law...

A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this...

A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this...

A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this...

Synchronous couplings of reflected Brownian motions in smooth domains (2005)

A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this...

Burdzy, Krzysztof, Chen, Zhen-Qing, Jones, Peter

For every bounded planar domain $D$ with a smooth boundary, we define a `Lyapunov exponent' $\Lambda(D)$ using a fairly explicit formula. We consider two reflected Brownian motions in $D$, driven by...

Uniqueness for reflecting brownian motion in lip domains (2005)

Bass, Richard F., Burdzy, Krzysztof, Chen, Zhen-Qing

A Gaussian Oscillator (2004)

Burdzy, Krzysztof; University Of Washington; Burdzy@math.washington.edu, White, David; University Of Washington; White@math.washington.edu

We present a stochastic process with sawtooth paths whose distribution is given by a simple rule and whose stationary distribution is Gaussian. The process arose in a natural way in research on...

Lenses in skew Brownian flow (2004)

Burdzy, Krzysztof, Kaspi, Haya

We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the...

The "hot spots" problem in planar domains with one hole (2004)

The heat equation and reflected Brownian motion in time-dependent domains (2004)

There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside...

Burdzy, Krzysztof, Chen, Zhen-Qing, Sylvester, John

The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "noncylindrical domains,'' and its connections with partial differential...

The Heat Equation And Reflected Brownian Motion In Time-Dependent Domains (2004)

Krzysztof Burdzy, Zhen-qing Chen, John Sylvester

this paper, for example, a Feynman--Kac type formula, are the basis for several effective quantitative and qualitative arguments in the second paper in this series, Burdzy, Chen and Sylvester (2003)....

Stable processes have thorns (2003)

Burdzy, Krzysztof, Kulczycki, Tadeusz

Let $X(t)$ be the symmetric $\alpha$-stable process in $\R$, $\alpha \in (0,2)$, $d \ge 2$. For $f\dvtx (0,1) \to (0,\infty)$ let $D(f)$ be the thorn $\{x \in \R\dvtx x_{1} \in (0,1),\allowbreak...

Censored Stable Processes (2003)

Krzysztof Bogdan, Krzysztof Burdzy, Zhen-qing Chen

We present several constructions of a "censored stable process" in an open set D , i.e., a symmetric stable process which is not allowed to jump outside D.

On Nodal Lines of Neumann Eigenfunctions (2002)

Atar, Rami; Technion - Israel Institute Of Technology; Atar@ee.technion.ac.il, Burdzy, Krzysztof; University Of Washington; Burdzy@math.washington.edu

We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.

On nodal lines of Neumann eigenfunctions (2002)

Erratum to “The supremum of brownian local times on Hölder curves” (2002)

We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain. The technique is based on the `mirror coupling' of reflected Brownian...

Brownian motion reflected on Brownian motion”, Probability Theory and Related Fields (2002)

Krzysztof Burdzy, David Nualart

and excursion theory of Brownian motion re ected on Brownian motion. Re ected Brownian motion in a domain with a time-varying boundary has appeared in several articles (Bass and Burdzy [BB1],...

Local time flow related to skew brownian motion (2001)

Burdzy, Krzysztof, Chen, Zhen-Qing

We define a local time flow of skew Brownian motions ,that is, a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but...

Coalescence of skew brownian motions (2001)

Barlow, Martin T., Burdzy, Krzysztof, Kaspi, Haya, Mandelbaum, Avi

The supremum of brownian local times on Hölder curves (2001)

Censored stable processes (2001)

Krzysztof Bogdan, Krzysztof Burdzy, Zhen-qing Chen

We present several constructions of a \censored stable process " in an open set D R n, i.e., a symmetric stable process which is not allowed to jump outside D. We address the question of...

Fiber Brownian motion and the "hot spots" problem (2000)

Efficient Markovian couplings: examples and counterexamples (2000)

Burdzy, Krzysztof, Kendall, Wilfrid S.

In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the...

Super-Brownian motion with reflecting historical paths (2000)

Burdzy, Krzysztof, Gall, Jean-Francois Le

We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions...

Variably Skewed Brownian Motion (2000)

Barlow, Martin; University Of British Columbia; Barlow@math.ubc.ca, Burdzy, Krzysztof; University Of Washington; Burdzy@math.washington.edu, Kaspi, Haya; Technion Institute; Iehaya@tx.technion.ac.il, Mandelbaum, Avi; Technion Institute; Avim@tx.technion.ac.il

Given a standard Brownian motion $B$, we show that the equation X_t = x_0 + B_t + beta(L_t^X), t geq 0, has a unique strong solution $X$. Here $L^X$ is the symmetric local time of $X$ at $0$, and...

The supremum of Brownian local times on Holder curves (2000)

Bass, Richard, Burdzy, Krzysztof

For $f: [0,1]\to \R$, we consider $L^f_t$, the local time of space-time Brownian motion on the curve $f$. Let $\sS_\al$ be the class of all functions whose H\"older norm of order $\al$ is less than...

Fiber Brownian Motion And The "Hot Spots" Problem (2000)

Coalescence of skew Brownian motions (1999)

. We show that in some planar domains both extrema of the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of "fiber Brownian motion," a...

Barlow, Martin, Burdzy, Krzysztof, Kaspi, Haya, Mandelbaum, Avi

We prove that two skew Brownian motions with the same skewness parameter (different from 0) and driven by the same Brownian motion coalesce a.s.

A counterexample to the "hot spots'' conjecture (1999)

Burdzy, Krzysztof, Werner, Wendelin

We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with...

Stochastic Bifurcation Models (1999)

A counterexample to the "hot spots" conjecture (1999)

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray–Knight...

Werner, Wendelin, Burdzy, Krzysztof

Statistics (1999)

Sharon Browning, Elizabeth Thompson, Elizabeth Thompson, Krzysztof Burdzy, Philip Green

Reading Committee: Date: and that any and all revisions required by the final examining committee have been made.

Local time flow related to skew Brownian motion (preprint (1999)

Local Time Flow Related To Skew Brownian Motion (1999)

Summary. We dene a local time ow of skew Brownian motions, i.e., a family of solutions to the stochastic dierential equation dening the skew Brownian motion, starting from dierent points but driven...

Local time flow related to skew Brownian motion (preprint (1999)

Introduction. We will present some results on a family of local time processes, including a new Ray-Knight-type theorem. The results and techniques are directly inspired by those in a paper of...

Brownian motion in a Brownian crack (1998)

We define a local time flow of skew Brownian motions, that is, a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but...

Burdzy, Krzysztof, Khoshnevisan, Davar

Let D be the Wiener sausage of width $\varepsilon$ around two-sided Brownian motion. The components of two-dimensional reflected Brownian motion in D converge to one-dimensional Brownian motion and...

Weak Convergence of Reflected Brownian Motions (1998)

Burdzy, Krzysztof; University Of Washington; Burdzy@math.washington.edu, Chen, Zhen-Qing; Cornell University; Zchen@math.cornell.edu

We show that if a sequence of domains $D_k$ increases to a domain $D$ then the reflected Brownian motions in $D_k$'s converge to the reflected Brownian motion in $D$, under mild technical assumptions.

Sets avoided by Brownian motion (1998)

Adelman, Omer, Burdzy, Krzysztof, Pemantle, Robin

A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability...

A counterexample to the "hot spots" conjecture (1998)

Burdzy, Krzysztof, Werner, Wendelin

We construct a counterexample to the ``hot spots'' conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with...

Stochastic bifurcation models (1998)

Brownian Motion in a Brownian Crack (1998)

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight...

Krzysztof Burdzy, Davar Khoshnevisan

. Let D be the Wiener sausage of width " around two-sided Brownian motion. The components of 2-dimensional reflected Brownian motion in D converge to 1-dimensional Brownian motion and iterated...

Efficient Markovian couplings: examples and counterexamples (1998)

Variably Skewed Brownian Motion (1998)

In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the...

Martin Barlow, Krzysztof Burdzy, Haya Kaspi, Avi Mandelbaum

Given a standard Brownian motion B, we show that the equation X t = x 0 +B t + fi(L X t ) ; t 0 ; has a unique strong solution X. Here L X is the symmetric local time of X at 0, and fi is a given...

Efficient Markovian couplings: examples and counterexamples (1998)

Krzysztof Burdzy, Wilfrid S. Kendall

In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the...

Positivity of Brownian Transition Densities (1997)

Barlow, Martin; University Of British Columbia; Barlow@math.ubc.ca, Bass, Richard F.; University Of Washington; Bass@math.washington.edu, Burdzy, Krzysztof; University Of Washington; Burdzy@math.washington.edu

Let $B$ be a Borel subset of $R^d$ and let $p(t,x,y)$ be the transition densities of Brownian motion killed on leaving $B$. Fix $x$ and $y$ in $B$. If $p(t,x,y)$ is positive for one $t$, it is...

On minimal parabolic functions and time-homogeneous parabolic h-transforms (1997)

Burdzy, Krzysztof, Salisbury, Thomas S.

Does a minimal harmonic function $h$ remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin semi-infinite tubes $D\subset \R^d$ of variable width...

Sets avoided by Brownian motion (1997)

Adelman, O., Burdzy, Krzysztof, Pemantle, Robin

Any fixed cylinder is hit almost surely by a 3-dimensional Brownian motion, but is there a random cylinder that is in the complement? We answer this for cylinders, and then replacing a cylinder with...

On Minimal Parabolic Functions And Time-Homogeneous Parabolic h-Transforms (1997)

Krzysztof Burdzy, Thomas S. Salisbury

. Does a minimal harmonic function h remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin semi-infinite tubes D ae R d of variable width and...

Itô formula for an asymptotically $4$-stable process (1996)

Burdzy, Krzysztof, M{\polhk{a}}drecki, Andrzej

We study an asymptotically 4-stable process. The main result is an Itô type formula.

Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times (1996)

Bass, Richard F.; University Of Washington; Bass@math.washington.edu, Burdzy, Krzysztof; University Of Washington; Burdzy@math.washington.edu

Let $B$ be a Borel subset of $R^d$ with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting $B$. Let $A_1$ be the time spent by Brownian...

No triple point of planar Brownian motion is accessible (1996)

Burdzy, Krzysztof, Werner, Wendelin

We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed time interval contains almost surely no triple point of this Brownian path.

Eigenvalue expansions for Brownian motion with an application to occupation times (1996)

Fast Equilibrium Selection by Rational Players Living in a Changing World (1996)

b i l i t y

Krzysztof Burdzy, David M. Frankel, Ady Pauzner

We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk dominant...

Sur quelques filtrations et transformations browniennes (1995)

Attal, Stéphane, Burdzy, Krzysztof, Émery, Michel, Hu, Yue-Yun

The level sets of iterated brownian motion (1995)

Burdzy, Krzysztof, Khoshnevisan, Davar

Non-Increase Of Brownian Motion And Random Coverings (1995)

Excursion laws and exceptional points on brownian paths (1993)

. A new proof of the non-increase of Brownian paths is given. Comment added January 18, 1995 The argument given in this note is based on an idea which has already appeared in print. See...

Non-polar points for reflected brownian motion (1993)

Burdzy, Krzysztof, Marshall, Donald E.

Hitting a boundary point with reflected brownian motion (1992)

Burdzy, Krzysztof, Marshall, Donald

Hölder domains and the boundary Harnack principle (1991)

Bañuelos, Rodrigo, Bass, Richard F., Burdzy, Krzysztof

Minimal fine derivatives and Brownian excursions (1990)