4 papers
Diffusion limits of cyclic finite-velocity random motions along vector fields
Olga Aryasova, Ilya Pavlyukevich, Yusif Sualah
We investigate diffusion approximations for a class of multivariate inhomogeneous finite-velocity random motions motivated by models of active particles. A particle alternates cycl…
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)…
Limit theorems for sticky SDEs with local times and applications to stochastic homogenization
Olga Aryasova, Ilya Pavlyukevich, Andrey Pilipenko
In this paper, we establish a general convergence theorem for solutions of multivariate stochastic differential equations with countably many singular terms expressed as integrals…
How to simulate Lévy flights in a steep potential: An explicit splitting numerical scheme
Ilya Pavlyukevich, Olga Aryasova, Alexei Chechkin +1
We propose an effective explicit numerical scheme for simulating solutions of stochastic differential equations with confining superlinear drift terms, driven by multiplicative hea…