Diffusivity bounds for 1d Brownian polymers (2009)
Tarres, Pierre, Toth, Balint, Valko, Benedek
We study the asymptotic behavior of a self interacting one dimensional Brownian polymer first introduced by Durrett and Rogers. The polymer describes a stochastic process with a drift which is a...
Continuous time `true' self-avoiding random walk on Z (2009)
We consider the continuous time version of the `true' or `myopic' self-avoiding random walk with site repulsion in 1d. The Ray-Knight-type method which was applied to the discrete time and edge...
Erdos-Renyi random graphs + forest fires = self-organized criticality (2009)
Rath, Balazs; Budapest University Of Technology; Rathb@math.bme.hu, Toth, Balint; Budapest University Of Technology; Balint@math.bme.hu
We modify the usual Erdos-Renyi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the...
Self-repelling random walk with directed edges on Z (2008)
Veto, Balint; Budapest University Of Technology; Vetob@math.bme.hu, Toth, Balint; Budapest University Of Technology; Balint@math.bme.hu
We consider a variant of self-repelling random walk on the integer lattice Z where the self-repellence is defined in terms of the local time on oriented edges. The long-time asymptotic scaling of...
Erdos-Renyi random graphs + forest fires = self-organized criticality (2008)
We modify the usual Erdos-Renyi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the...
Self-repelling random walk with directed edges on Z (2008)
We consider a variant of self-repelling random walk on the integer lattice Z where the self-repellence is defined in terms of the local time on oriented edges. The long-time asymptotic scaling of...
Skorohod-reflection of Brownian Paths and BES^3 (2007)
Let B(t), X(t) and Y(t) be independent standard 1d Borwnian motions. Define X^+(t) and Y^-(t) as the trajectories of the processes X(t) and Y(t) pushed upwards and, respectively, downwards by B(t),...
Modeling the Epps effect of cross correlations in asset prices (2007)
Toth, Bence, Toth, Balint, Kertesz, Janos
We review the decomposition method of stock return cross-correlations, presented previously for studying the dependence of the correlation coefficient on the resolution of data (Epps effect). Through...
Favourite Sites of Simple Random Walk (2000)
Introduction Let (S(n), n ) be a simple symmetric random walk on Z with S(0) = 0. Define #(n, x) := #{0 n : S(k) = x}, (1.1) which is referred to as the (site) local time of the random walk. For each...
Modeling the Epps effect of cross correlations in asset prices
Bence Toth, Balint Toth, Janos Kertesz
We review the decomposition method of stock return cross-correlations, presented previously for studying the dependence of the correlation coefficient on the resolution of data (Epps effect). Through...