101 citations · 281 across the 11 of their papers we have counts for
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From intersection local time to the Rosenblatt process
Tomasz Bojdecki, Luis G. Gorostiza, Anna Talarczyk
The Rosenblatt process was obtained by Taqqu (1975) from convergence in distribution of partial sums of strongly dependent random variables. In this paper we give a particle pictur…
Oscillatory Fractional Brownian Motion and Hierarchical Random Walks
Tomasz Bojdecki, Luis G. Gorostiza, Anna Talarczyk
We introduce oscillatory analogues of fractional Brownian motion, sub-fractional Brownian motion and other related long range dependent Gaussian processes, we discuss their propert…
Particle picture interpretation of some Gaussian processes related to fractional Brownian motion
Tomasz Bojdecki, Anna Talarczyk
We construct fractional Brownian motion (fBm), sub-fractional Brownian motion (sub-fBm), negative sub-fractional Brownian motion (nsfBm) and the odd part of fBm in the sense of Dzh…
Number variance for hierarchical random walks and related fluctuations
Tomasz Bojdecki, Luis G. Gorostiza, Anna Talarczyk
We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The…
Particle systems with quasi-homogeneous initial states and their occupation time fluctuations
Tomasz Bojdecki, Luis G. Gorostiza, Anna Talarczyk
Occupation time fluctuation limits of particle systems in R^d with independent motions (symmetric stable Levy process, with or without critical branching) have been studied assumin…
Occupation times of branching systems with initial inhomogeneous Poisson states and related superprocesses
Tomasz Bojdecki, Luis G. Gorostiza, Anna Talarczyk
The -branching particle system consists of particles moving in according to a symmetric -stable Lévy process , splitting with a critical -br…