5 citations · 15 across the 9 of their papers we have counts for
13 papers · 1 filter
On weak solution of SDE driven by inhomogeneous singular Lévy noise
Tadeusz Kulczycki, Alexei Kulik, Michał Ryznar
We study a time-inhomogeneous SDE in driven by a cylindrical Lévy process with independent coordinates which may have different scaling properties. Such a structure of the d…
On regularization by a small noise of multidimensional ODEs with non-Lipschitz coefficients
Alexei Kulik, Andrey Pilipenko
In this paper we solve a selection problem for multidimensional SDE , where the drift and diffu…
Construction and heat kernel estimates of general stable-like Markov processes
V. Knopova, A. Kulik, R. Schilling
A stable-like process is a Feller process taking values in and whose generator behaves, locally, like an -stable Lévy process, but the index …
First order convergence of weak Wong--Zakai approximations of Lévy driven Marcus SDEs
Tetyana Kosenkova, Alexei Kulik, Ilya Pavlyukevich
For solutions of Lévy-driven Marcus stochastic differential equations we study the Wong--Zakai type time discrete approximations $\bar X=(\bar X_{kh})_{0\leq…
Well-Posedness, Stability, and Sensitivities for Stochastic Delay Equations: A Generalized Coupling Approach
Alexei Kulik, Michael Scheutzow
We develop a new generalized coupling approach to the study of stochastic delay equations with Hölder continuous coefficients, for which analytical PDE-based methods are not availa…
Approximation in law of locally -stable Lévy-type processes by non-linear regressions
Alexei Kulik
We study a real-valued Lévy-type process , which is locally -stable in the sense that its jump kernel is a combination of a `principal' (state dependent) -stable part with…