2 citations · 2 across the 4 of their papers we have counts for
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Functional limit theorems for perturbed random walks
Andrey Pilipenko
We consider scaling limits of integer-valued random walks whose transition probabilities are translation-invariant everywhere except on a set that we will call a membrane or an int…
Functional central limit theorem for superdiffusive SDEs with stable noise
Aleksandar Mijatović, Andrey Pilipenko, Isao Sauzedde
This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an -stable process.
Explosion and implosion of birth-and-death continuous-time random walks
Andrey Pilipenko, Vadym Tkachenko
We provide necessary and sufficient conditions for explosion and implosion of birth-and-death (non-Markov) continuous-time random walks. In other words, we obtain conditions for $\…
On multidimensional locally perturbed standard random walks
Congzao Dong, Alexander Iksanov, Andrey Pilipenko
Let be a positive integer and a set in , which contains finitely many points with integer coordinates. We consider a standard random walk perturbed on the…
Walsh's Brownian Motion and Donsker Scaling Limits of Perturbed Random Walks
Ilya Pavlyukevich, Andrey Pilipenko
In this paper we study Markov chains with the state space given by the coordinate axes of , , whose step sizes on each positive half-axis are distributed acc…