680 citations · 965 across the 33 of their papers we have counts for
27 papers · 1 filter
Heterogeneous diffusion process with power-law nonlinearity
Jorge E. Cardona, Ilya Pavlyukevich
In this paper, we study solutions of the heterogeneous diffusion process with power-law nonlinearity governed by the stochastic differential equation $\mathrm{d}X_t= |X_t|^α\,\math…
A Tail-Respecting Splitting Numerical Scheme for Lévy-Driven SDEs With Superlinear Drifts
Olga Aryasova, Oleksii Kulyk, Ilya Pavlyukevich
We present an explicit numerical approximation scheme, denoted by , for the effective simulation of solutions to a multivariate stochastic differential equation (SDE)…
Strong uniform Wong--Zakai approximations of Lévy-driven Marcus SDEs
Ilya Pavlyukevich, Sooppawat Thipyarat
For a solution of a Lévy-driven -dimensional Marcus (canonical) stochastic differential equation, we show that the Wong--Zakai type approximation scheme has a strong c…
Stochastic energy-balance model with a moving ice line
Ilya Pavlyukevich, Marian Ritsch
In [SIAM J. Appl. Dyn. Sys., 12(4):2068--2092, 2013], Widiasih proposed and analyzed a deterministic one-dimensional Budyko-Sellers energy-balance model with a moving ice-line. In…
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…
Stochastic selection problem for a Stratonovich SDE with power non-linearity
Ilya Pavlyukevich, Georgiy Shevchenko
In our paper [Bernoulli 26(2), 2020, 1381-1409], we found all strong Markov solutions that spend zero time at of the Stratonovich stochastic differential equation $d X=|X|^α\ci…