680 citations · 965 across the 33 of their papers we have counts for
36 papers
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…
Early warning signs of critical transitions -- The -stable case
Lucia S. Layritz, Ilya Pavlyukevich, Anja Rammig +1
Statistical early warning signs can be used to identify an approaching bifurcation in stochastic dynamical systems and are now regularly employed in applications concerned with the…
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…