15 citations · 71 across the 35 of their papers we have counts for
37 papers
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…
Boundary Approximation for Sticky Jump-Reflected Processes on the Half-Line
Andrey Pilipenko, Andrey Sarantsev
The Skorokhod reflection was used in 1961 to create a reflected diffusion on the half-line. Later, it was used for processes with jumps such as reflected Lévy processes. Like a Bro…
Homogenization of a multivariate diffusion with semipermeable interfaces
Olga Aryasova, Ilya Pavlyukevich, Andrey Pilipenko
We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperpl…
On a discrete approximation of a skew stable Lévy process
Congzao Dong, Oleksandr Iksanov, Andrey Pilipenko
Iksanov and Pilipenko (2023) defined a skew stable Lévy process as a scaling limit of a sequence of perturbed at symmetric stable Lévy processes (continuous-time processes). He…
The zero-noise limit of SDEs with drift
Ulrik Skre Fjordholm, Markus Musch, Andrey Pilipenko
We study the zero-noise limit for autonomous, one-dimensional ordinary differential equations with discontinuous right-hand sides. Although the deterministic equation might have in…
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…