2 citations · 2 across the 6 of their papers we have counts for
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Low-dimensional Cox-Ingersoll-Ross process
Yuliya Mishura, Andrey Pilipenko, Anton Yurchenko-Tytarenko
The present paper investigates Cox-Ingersoll-Ross (CIR) processes of dimension less than 1, with a focus on obtaining an equation of a new type including local times for the square…
On a skew stable Lévy process
Alexander Iksanov, Andrey Pilipenko
The skew Brownian motion is a strong Markov process which behaves like a Brownian motion until hitting zero and exhibits an asymmetry at zero. We address the following question: wh…
A functional limit theorem for for excited random walks
Andrey Pilipenko
We consider the limit behavior of an excited random walk (ERW), i.e., a random walk whose transition probabilities depend on the number of times the walk has visited to the current…
On a limit behavior of a random walk with modifications at zero
Andrey Pilipenko, Vladislav Khomenko
We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle…
On perturbations of an ODE with non-Lipschitz coefficients by a small self-similar noise
Andrey Pilipenko, Frank Norbert Proske
We study the limit behavior of differential equations with non-Lipschitz coefficients that are perturbed by a small self-similar noise. It is proved that the limiting process is eq…
Functional limit theorems for the maxima of perturbed random walks and divergent perpetuities in the -topology
Alexander Iksanov, Andrey Pilipenko, Igor Samoilenko
Let , be a sequence of i.i.d. two-dimensional random vectors. In the earlier article Iksanov and Pilipenko (2014) weak convergence in the -topolo…