A. Kulik

activity

20122021

most citedPoincare inequality and exponential integrability of the hitting times of a Markov process

5 citations · 15 across the 9 of their papers we have counts for

collaborators

Showing 2020 · math.PRShow all

5 papers · 2 filters

math.PR2020

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 $d X^{ε} (t) = a (X^{ε} (t)) d t + ε σ (X^{ε} (t)) d W (t)$ , where the drift and diffu…

math.PR2020

Gradient formula for transition semigroup corresponding to stochastic equation driven by a system of independent Lévy processes

Alexei Kulik, Szymon Peszat, Enrico Priola

Let $(P_{t})$ be the transition semigroup of the Markov family $(X^{x} (t))$ defined by SDE $d X = b (X) d t + d Z, X (0) = x,$ where $Z = (Z_{1}, \dots, Z_{d})^{*}$ is a syste…

math.PR2020★ 4 cited

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 $(X_{t})_{t \geq 0}$ taking values in $R^{d}$ and whose generator behaves, locally, like an $α$ -stable Lévy process, but the index $α$ …

math.PR2020

Moment bounds for dissipative semimartingales with heavy jumps

Alexei Kulik, Ilya Pavlyukevich

In this paper we show that if large jumps of an Itô-semimartingale $X$ have a finite $p$ -moment, $p > 0$ , the radial part of its drift is dominated by $- ∣ X ∣^{κ}$ for some $κ \geq - 1$ , a…

math.PR2020

First order convergence of weak Wong--Zakai approximations of Lévy driven Marcus SDEs

Tetyana Kosenkova, Alexei Kulik, Ilya Pavlyukevich

For solutions $X = (X_{t})_{t \in [0, T]}$ of Lévy-driven Marcus stochastic differential equations we study the Wong--Zakai type time discrete approximations $\bar X=(\bar X_{kh})_{0\leq…