3 papers
math.PR2026
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)…
math.PR2025
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\,\mat…
math.PR2025
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…