Jay Rosen

An almost sure limit theorem for Wick powers of Gaussian differences quotients (2009)

We give a stochastic calculus proof of the Central Limit Theorem \[ {\int (L^{x+h}_{t}- L^{x}_{t})^{2} dx- 4ht\over h^{3/2}} \stackrel{\mathcal{L}}{\Longrightarrow}c(\int (L^{x}_{t})^{2} dx)^{1/2}...

A CLT for the $L^{2}$ norm of increments of local times of L\'evy processes as time goes to infinity (2009)

Let G={G(x), x\in R_+}, G(0)=0, be a mean zero Gaussian process with $E(G(x)-G(y))^2=\sigma ^2(x-y) $. Let $ \rho (x)= \frac12{d^{2}\over dx^2}\sigma^2(x)$, $x\ne 0 $. When $\rho^{k}$ is integrable...

A CLT for the third integrated moment of Brownian local time increments (2009)

Let $X=\{X_{t},t\in R_{+}\}$ be a symmetric L\'{e}vy process with local time $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$. When the L\'{e}vy exponent $\psi(\la)$ is regularly varying at zero with...

A CLT for the $L^{2}$ moduli of continuity of local times of Levy processes (2009)

Let $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$ denote the local time of Brownian motion. Our main result is to show that for each fixed $t$ $${\int (L^{x+h}_t- L^x_t)^3 dx-12h\int (L^{x+h}_t -...

A CLT for the L^{2} modulus of continuity of Brownian local time (2009)

Let $X=\{X_{t},t\in R_{+}\}$ be a symmetric L\'evy process with local time $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$. When the L\'evy exponent $\psi(\la)$ is regularly varying at infinity with...

Chen, Xia, Li, Wenbo, Marcus, Michael B., Rosen, Jay

Let $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$ denote the local time of Brownian motion and \[ \alpha_{t}:=\int_{-\infty}^{\infty} (L^{x}_{t})^{2} dx . \] Let $\eta=N(0,1)$ be independent of...

Infinite Divisibility of Gaussian Squares with Non-zero Means (2008)

Marcus, Michael B.; The City College Of CUNY; Mbmarcus@earthlink.net, Rosen, Jay; The College Of Staten Island Of CUNY; Jrosen3@earthlink.net

We give necessary and sufficient conditions for a Gaussian vector with non-zero mean, to have infinitely divisible squares for all scalar multiples of the mean, and show how the this vector is...

Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in $R^{2}$ with non--zero mean (2008)

Cover times for Brownian motion and (2008)

Let $G=(G_{1},G_{2})$ be a Gaussian vector in $R^{2}$ with $EG_{1}G_{2}\neq 0$. Let $c_{1},c_{2}\in R^{1}$. A necessary and sufficient condition for...

Laws of the Iterated Logarithm for Triple Intersections of Three Dimensional Random Walks (2008)

random walks in two dimensions

Jay Rosen, Abstact Letx {xn, X′ {x, Jay Rosen

E l e c t r o n

z (2007)

Laws of the Iterated Logarithm for Triple Intersections of Random Walks on Z 3 (2007)

Let (x; r) denote the occupation measure of the ball of radius r centered at x for Brownian motion fW t g 0t1 in IR d; d 2. We prove that for any analytic set E in [0; 1], we have inf t2E lim inf r!0...

Dirichlet Processes and an Intrinsic Characterization of Renormalized Intersection Local Times (2007)

Let X = {X n , n # 1}, X # = {X # n , n # 1} and X ## = {X ## n , n # 1} be three independent copies of a symmetric random walk in Z 3 with E(|X 1 | 2 log + |X 1 |) < #. In this paper we study the...

Additive functionals of several Lévy processes and self-intersection local times (2007)

We show that the n-th order renormalized self-intersection local time # n (µ; t) for the symmetric stable process in R 2 , where the n-fold multiple points are weighted by an arbitrary measure µ,...

Michael B, Michael B. Marcus, Jay Rosen

Di#erent extentons of an isomorphism theorem of Dynkin are developed and are used to study two distinct but related families of functionals of Levy processes; n-fold "near-intersections" of...

Yuval Peres, (2007)

Yuval Peres, Jay Rosen, Ofer Zeitouni

this paper, log 2 stands for the logarithm to the base 2.

L E C T R O N I C (2007)

Vol Paper No, Jay Rosen

Let X = fX n ; n 1g, X 0 = fX 0 n ; n 1g and X 00 = fX 00 n ; n 1g be three independent copies of a symmetric random walk in Z 3 with E(jX 1 j 2 log + jX 1 j) ! 1. In this paper we study the...

Capacitary moduli for Lvy processes and intersections (2007)

We introduce the concept of capacitary modulus for a set A C _ R d, which is a function h that provides simple estimates for the capacity of A with respect an arbitrary kernel f, estimates which...

OFER ZEITOUNI (2007)

Abstract. Let T (x; r) denote the occupation measure of the disc of radius r centered at x by planar Brownian motion run till time 1. We prove that sup jxj1 T (x; r)=(r 2

OFER ZEITOUNI x (2007)

Cover times for Brownian motion and random walks in two dimensions (2007)

Abstract. Let L X

Jay Rosen, Ofer Zeitouni

Abstract. Let T (x; ") denote the rst hitting time of the disc of radius " centered at x for Brownian motion on the two dimensional torus T 2 We prove that sup x2T 2 T (x;...

OFER ZEITOUNI x (2007)

Late Points For Random Walks In Two Dimensions Amir Dembo (2007)

Abstract. Let L X

3 (2007)

Yuval Peres, Jay Rosen, Ofer Zeitouni

Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for Brownian motion in IR 3. We prove that sup jxj1 T (x; r)=(r 2 j log rj) ! 16= 2 a.s. as r! 0, thus solving a...

Yuval Peres Jay, Jay Rosen

Let Tn(x) denote the time of rst visit of a point x on the lattice torus Z n = Z by the simple random walk. The size of the set of ; n-late points Ln() = fx 2 Z n : Tn (x) (n log n) g is...

Non normal CLTs for functions of the increments of Gaussian processes with convex increment's variance (2007)

Marcus, Michael, Rosen, Jay

Let G be a mean zero Gaussian processes with stationary increments and set \si ^2(|x-y|)= E(G(x)-G(y))^2. Let f be a function with Ef^{2}(\eta)

Frequent points for random walks in two dimensions (2007)

Bass, Richard F.; University Of Connecticut; Bass@math.uconn.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@earthlink.net

For a symmetric random walk in Z2 which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the...

Frequent points for random walks in two dimensions (2007)

Bass, Richard F.; University Of Connecticut; Bass@math.uconn.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@earthlink.net

For a symmetric random walk in Z2 which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the...

Bloggers vs journalists is over (2007)

CLT for L^{p} moduli of continuity of Gaussian processes (2006)

In this paper for the recent Blogging, Journalism & Credibility conference, Jay Rosen argues that the debate over whether blogging is journalism is over, but we haven't come to grips with the...

Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks (2006)

Let G=\{G(x),x\in R^1\} be a mean zero Gaussian processes with stationary increments and set \si ^2(|x-y|)= E(G(x)-G(y))^2. Let f be a symmetric function with Ef(\eta)

Bass, Richard F; University Of Connecticut; Bass@math.uconn.edu, Chen, Xia; University Of Tennessee; Xchen@math.utk.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@earthlink.net

We study moderate deviations for the renormalized self-intersection local time of planar random walks. We also prove laws of the iterated logarithm for such local times.

Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks (2006)

Bass, Richard F; University Of Connecticut; Bass@math.uconn.edu, Chen, Xia; University Of Tennessee; Xchen@math.utk.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@earthlink.net

We study moderate deviations for the renormalized self-intersection local time of planar random walks. We also prove laws of the iterated logarithm for such local times.

$L^p$ moduli of continuity of Gaussian processes and local times of symmetric L\'{e}vy processes (2006)

Frequent points for random walks in two dimensions (2006)

Let $X=\{X(t),t\in R_+\}$ be a real-valued symmetric L\'{e}vy process with continuous local times $\{L^x_t,(t,x)\in R_+\times R\}$ and characteristic function $Ee^{i\lambda...

Moderate deviations for the range of planar random walks (2006)

For a symmetric random walk in $Z^2$ which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the...

Bass, Richard F., Chen, Xia, Rosen, Jay

Given a symmetric random walk in $Z^2$ with finite second moments, let $R_n$ be the range of the random walk up to time $n$. We study moderate deviations for $R_n -E R_n$ and $E R_n -R_n$. We also...

Late points for random walks in two dimensions (2006)

Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer

Let $\mathcal{T}_{n}(x)$ denote the time of first visit of a point x on the lattice torus ℤn2=ℤ2/nℤ2 by the simple random walk. The size of the set of α, n-late points $\mathcal{L}_{n}(\alpha...

Large-time asymptotics for the density of a branching Wiener process (2005)

Révész, Pál, Rosen, Jay, Shi, Zhan

Given an ℝd-valued supercritical branching Wiener process, let ψ(A,T) be the number of particles in A⊂ℝd at time T (T=0,1,2,...). We provide a complete asymptotic expansion of ψ(A,T) as...

An almost sure invariance principle for the range of planar random walks (2005)

Large deviations for renormalized self-intersection local times of stable processes (2005)

For a symmetric random walk in Z2 with 2+δ moments, we represent |ℛ(n)|, the cardinality of the range, in terms of an expansion involving the renormalized intersection local times of a Brownian...

Bass, Richard, Chen, Xia, Rosen, Jay

We study large deviations for the renormalized self-intersection local time of d-dimensional stable processes of index \beta \in (2d/3,d]. We find a difference between the upper and lower tail. In...

Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks (2005)

Bass, Richard F., Chen, Xia, Rosen, Jay

Let B_n be the number of self-intersections of a symmetric random walk with finite second moments in the integer planar lattice. We obtain moderate deviation estimates for B_n - E B_n and E B_n- B_n,...

Large Deviations for Local Times of Stable Processes and Stable Random Walks in 1 Dimension (2005)

Chen, Xia; University Of Tennessee, USA; Xchen@math.utk.edu, Li, Wenbo; University Of Delaware, USA; Wli@math.udel.edu, Rosen, Jay; College Of Staten Island, CUNY, USA; Jrosen3@earthlink.net

In Chen and Li (2004), large deviations were obtained for the spatial $L^p$ norms of products of independent Brownian local times and local times of random walks with finite second moment. The...

Large Deviations for Local Times of Stable Processes and Stable Random Walks in 1 Dimension (2005)

Chen, Xia; University Of Tennessee, USA; Xchen@math.utk.edu, Li, Wenbo; University Of Delaware, USA; Wli@math.udel.edu, Rosen, Jay; College Of Staten Island, CUNY, USA; Jrosen3@earthlink.net

In Chen and Li (2004), large deviations were obtained for the spatial $L^p$ norms of products of independent Brownian local times and local times of random walks with finite second moment. The...

Large deviations for renormalized self-intersection local times of stable processes (2005)

Bass, Richard, Chen, Xia, Rosen, Jay

We study large deviations for the renormalized self-intersection local time of d-dimensional stable processes of index β∈(2d/3,d]. We find a difference between the upper and lower tail. In...

How large a disc is covered by a random walk in n steps? (2005)

Dembo, Amir, Peres, Yuval, Rosen, Jay

We show that the largest disc covered by a simple random walk (SRW) on $\mathbb{Z}^2$ after n steps has radius n^{1/4+o(1)}, thus resolving an open problem of R\'{e}v\'{e}sz [Random Walk in Random...

A random walk proof of the Erdos-Taylor conjecture (2005)

An Almost Sure Invariance Principle for Renormalized Intersection Local Times (2005)

For the simple random walk in Z^2 we study those points which are visited an unusually large number of times, and provide a new proof of the Erdos-Taylor conjecture describing the number of visits to...

Bass, Richard F.; University Of Connecticut, USA; Bass@math.uconn.edu, Rosen, Jay; City University Of New York, USA; Jrosen3@earthlink.net

Let beta_k(n) be the number of self-intersections of order k, appropriately renormalized, for a mean zero planar random walk with 2+delta moments. On a suitable probability space we can construct the...

Exponential asymptotics for intersection local times of stable processes and random walks (2005)

Chen, Xia, Rosen, Jay

Frequently visited sets for random walks (2004)

Csáki, Endre, Földes, Antónia, Révész, Pál, Rosen, Jay, Shi, Zhan

We study the occupation measure of various sets for a symmetric transient random walk in $Z^d$ with finite variances. Let $\mu^X_n(A)$ denote the occupation time of the set $A$ up to time $n$. It is...

Large time asymptotics for the density of a branching Wiener process (2004)

Révész, Pál, Rosen, Jay, Shi, Zhan

Given an R^d-valued supercritical branching Wiener process, let D(A,T) be the number of particles in a subset A of R^d at time T, (T=0,1,2,...). We provide a complete asymptotic expansion of D(A,T)...

Cover times for Brownian motion and random walks in two dimensions (2004)

Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer

Let $\TT(x,\eps)$ denote the first hitting time of the disc of radius $\eps$ centered at $x$ for Brownian motion on the two dimensional torus $\Bbb{T}^2$. We prove that $\sup_{x\in \Bbb{T}^2}...

An almost sure invariance principle for renormalized intersection local times (2004)

An almost sure invariance principle for the range of planar random walks (2004)

Let \beta_k(n) be the number of self-intersections of order k, appropriately renormalized, for a mean zero random walk X_n in Z^2 with 2+\delta moments. On a suitable probability space we can...

Brownian Motion on Compact Manifolds: Cover Time and Late Points (2003)

For a symmetric random walk in $Z^2$ with $2+\delta$ moments, we represent $|\mathcal{R}(n)|$, the cardinality of the range, in terms of an expansion involving the renormalized intersection local...

Dembo, Amir; Stanford University; Amir@math.stanford.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@earthlink.net

Let $M$ be a smooth, compact, connected Riemannian manifold of dimension $d>2$ and without boundary. Denote by $T(x,r)$ the hitting time of the ball of radius $r$ centered at $x$ by Brownian motion...

Brownian Motion on Compact Manifolds: Cover Time and Late Points (2003)

Dembo, Amir; Stanford University; Amir@math.stanford.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@earthlink.net

Let $M$ be a smooth, compact, connected Riemannian manifold of dimension $d>2$ and without boundary. Denote by $T(x,r)$ the hitting time of the ball of radius $r$ centered at $x$ by Brownian motion...

Late points for random walks in two dimensions (2003)

Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer

Let $\mathcal{T}_n(x)$ denote the time of first visit of a point $x$ on the lattice torus $\mathbb {Z}_n^2=\mathbb{Z}^2/n\mathbb{Z}^2$ by the simple random walk. The size of the set of $\alpha$,...

Brownian Motion on Compact Manifolds: Cover Time and Late Points (2002)

Amir Dembo, Yuval Peres, Jay Rosen

Let M be a smooth, compact, connected Riemannian manifold of dimension d ≥ 3 and without boundary. Denote by T(x, ε) the hitting time of the ball of radius ε centered...

Cover Times for Brownian Motion and Random Walks in Two Dimensions (2001)

Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer

Let T(x,r) denote the first hitting time of the disc of radius r centered at x for Brownian motion on the two dimensional torus. We prove that sup_{x} T(x,r)/|log r|^2 --> 2/pi as r --> 0. The same...

Thick points for intersections of planar sample paths (2001)

Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer

Let $L_n^{X}(x)$ denote the number of visits to $x \in {\bf Z}^2$ of the simple planar random walk $X$, up till step $n$. Let $X'$ be another simple planar random walk independent of $X$. We show...

Dirichlet processes and an intrinsic characterization of renormalized intersection local times (2001)

Cover times for Brownian motion and random walks in two dimensions (2001)

A Ray-Knight theorem for symmetric Markov processes (2000)

Let T (x; ") denote the rst hitting time of the disc of radius " centered at x for Brownian motion on the two dimensional torus T 2 We prove that sup x2T 2 T (x; ")=j log...

Eisenbaum, Nathalie, Kaspi, Haya, Marcus, Michael B., Rosen, Jay, Shi, Zhan

Let $X$ be a strongly symmetric recurrent Markov process with state space $S$ and let $L_t^x$ denote the local time of $X$ at $X \in S$. For a fixed element 0 in the state space S, let $$ \tau(t) :=...

Thick points for spatial Brownian motion: multifractal analysis of occupation measure (2000)

Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer

Let $\mathscr{T}(x,r)$ denote the total occupation measure of the ball of radius $r$ centered at $x$ for Brownian motion in $\mathbb{R}^3$. We prove that $\sup_{|x|\leq1}\mathscr{T}(x,r)/(r^{2}|\log...

Thin points for brownian motion (2000)

Dembo, Amir, Peres, Yuval, Rosen, Jay, Zeitouni, Ofer

Additive Functionals of Several Lévy Processes and Intersection Local Times (1999)

Thick Points for Transient Symmetric Stable Processes (1999)

Different extensions of an isomorphism theorem of Dynkin are developed and are used to study two distinct but related families of functionals of Lévy processes; $n$-fold “near-intersections” of...

Dembo, Amir; Stanford University; Amir@stat.standford.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@idt.net, Zeitouni, Ofer; Technion; Zeitouni@ee.technion.ac.il

Let T(x,r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index $b<d$ in $R^d$ and K(b,d) denote the norm of the...

Thick Points for Transient Symmetric Stable Processes (1999)

Dembo, Amir; Stanford University; Amir@stat.standford.edu, Peres, Yuval; University Of California, Berkeley; Peres@stat.berkeley.edu, Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@idt.net, Zeitouni, Ofer; Technion; Zeitouni@ee.technion.ac.il

Let T(x,r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index $b<d$ in $R^d$ and K(b,d) denote the norm of the...

Joint continuity and a Doob-Meyer type decomposition for renormalized intersection local times (1999)

Thick points for transient symmetric stable processes, Elect (1999)

Thick Points for Planar Brownian Motion and the Erdös-Taylor Conjecture on Random Walk (1999)

Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index in IR d and ;d denote the norm of the convolution with its...

Thick Points for Transient Symmetric Stable Processes (1999)

Let T (x; r) denote the occupation measure of the disc of radius r centered at x by planar Brownian motion run till time 1. We prove that sup jxj1 T (x; r)=(r 2 j log rj 2 ) ! 2 a.s. as r ! 0, thus...

Occupation time large deviations for critical branching Brownian motion, super-Brownian motion and related processes (1998)

Let T (x, r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index # < d in IR d and # #,d denote the norm of the...

Deuschel, Jean-Dominique, Rosen, Jay

We derive a large deviation principle for the occupation time func-tional, acting on functions with zero Lebesgue integral, for both super-Brownian motion and critical branching Brownian motion in...

Functional laws of the iterated logarithm for local times of recurrent random walks on $Z^2$ (1998)

Csáki, Endre, Révész, Pál, Rosen, Jay

Thick Points for Spatial Brownian Motion: Multifractal Analysis of Occupation Measure (1998)

Amir Dembo Yuval, Yuval Peres, Jay Rosen, Ofer Zeitouni

Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for Brownian motion in IR 3 . We prove that sup jxj1 T (x; r)=(r 2 j log rj) ! 16=ß 2 a.s. as r ! 0, thus...

Laws of the Iterated Logarithm for Triple Intersections of Three Dimensional Random Walks (1997)

Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@idt.net

Let X = X_n, X' = X'_n, and X'' = X''_n, ngeq 1, be three independent copies of a symmetric three dimensional random walk with E(|X_1|^{2}log_+ |X_1|) finite. In this paper we study the asymptotics...

Laws of the Iterated Logarithm for Triple Intersections of Three Dimensional Random Walks (1997)

Rosen, Jay; College Of Staten Island, CUNY; Jrosen3@idt.net

Let X = X_n, X' = X'_n, and X'' = X''_n, ngeq 1, be three independent copies of a symmetric three dimensional random walk with E(|X_1|^{2}log_+ |X_1|) finite. In this paper we study the asymptotics...

Laws of the iterated logarithm for intersections of random walks on Z4 (1997)

Laws Of The Iterated Logarithm For Triple Intersections Of Three Dimensional Random Walks (1997)

Gaussian chaos and sample path properties of additive functionals of symmetric Markov processes (1996)

Let X = fX n ; n 1g, X 0 = fX 0 n ; n 1g and X 00 = fX 00 n ; n 1g be three independent copies of a symmetric random walk in Z 3 with E(jX 1 j 2 log + jX 1 j) ! 1. In this paper we study the...

Random Fourier series and continuous additive functionals of Lévy processes on the torus (1996)

Let X be a strongly symmetric Hunt process with $\alpha$-potential density $u^\alpha(x,y). Let $$ {\mathcal G}_{\alpha}^2 = \left\{\mu | \int\int(u^\alpha (x,y))^2 d\mu(x)\; d\mu (y)

Laws of the iterated logarithm for the local times of recurrent random walks on Z2 and of Lévy processes and Random walks in the domain of attraction of Cauchy random variables (1994)

Let X be an exponentially killed Lévy process on $T^n$ , the $n$ -dimensional torus, that satisfies a sector condition. (This includes symmetric Lévy processes.) Let$\mathscr{F}_e$ denote the...

The impossible press : American journalism and the decline of public life / (1986)

Rosen, Jay.

Typescript.

A local time approach to the self-intersections of Brownian paths in space (1983)

Existence of the critical point in $\phi^{4}$ field theory (1976)

McBryan, Oliver A., Rosen, Jay

Global support properties of stationary ergodic processes (1975)

Rosen, Jay, Simon, Barry

The intersection local time of fractional Brownian motion in the plane

Thin Points for Brownian Motion

We show how to renormalize the intersection local time of fractional Brownian motion of index [beta] in the plane, whenÂ½< [beta]

Multiple Wick Product Chaos Processes

Let T (x; r) denote the occupation measure of the ball of radius r centered at x for Brownian motion fW t g 0t1 in IR d ; d 2. We prove that for any analytic set E in [0; 1], we have inf t2E lim inf...

Michael B. Marcus, Jay Rosen

Let u(x) x # R q be a symmetric non-negative definite function which is bounded away from zero but which may have u(0) = #. Let p x,# (·) be the density of an R q valued canonical normal random...

Laws of the Iterated Logarithm for Intersections of Random Walks on Z 4

Michael B. Marcus, Jay Rosen

Let X = {X n , n # 1}, X # = {X # n , n # 1} be two independent copies of a symmetric random walk in Z 4 with finite third moment. In this paper we study the asymptotics of I n , the number of...

Renormalized self-intersection local times and Wick power chaos processes

Michael B. Marcus, Jay Rosen, Michael B

Sufficient conditions are obtained for the continuity of renormalized self-intersection local times for the multiple intersections of a large class of strongly symmetric Lévy processes in R m , m =...

Thick Points for Transient Symmetric Stable Processes

Thick Points for Spatial Brownian Motion: Multifractal Analysis of Occupation Measure

Let T (x; r) denote the total occupation measure of the ball of radius r centered at x for a transient symmetric stable processes of index fi ! d in IR d and fi;d denote the norm of the convolution...