A. Kulik

activity

20122020

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

5 citations · 10 across the 6 of their papers we have counts for

collaborators

8 papers

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.PR2016★ 2 cited

Large deviation principle for one-dimensional SDEs with discontinuous coefficients

Alexei Kulik, Daryna Sobolieva

We establish the large deviation principle for solutions of one-dimensional SDEs with discontinuous coefficients. The main statement is formulated in a form similar to the classica…

math.PR2016

Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance

Alexei Kulik, Daryna Sobolieva

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $ε W$ as $ε \to 0$ .

math.ST2016

Long time behavior of stochastic hard ball systems

Patrick Cattiaux, Myriam Fradon, Alexei M. Kulik +1

We study the long time behavior of a system of $n = 2, 3$ Brownian hard balls, living in $R^{d}$ for $d \geq 2$ , submitted to a mutual attraction and to elastic collisions.

math.PR2015

A martingale bound for the entropy associated with a trimmed filtration on $R^{d}$

Alexei Kulik, Taras Tymoshkevych

Using martingale methods, we provide bounds for the entropy of a probability measure on $R^{d}$ with the right-hand side given in a certain integral form. As a corollary, i…

math.PR2015★ 3 cited

Rates of approximation of nonsmooth integral-type functionals of Markov processes

Iu. Ganychenko, A. Kulik

We provide strong $L_{p}$ -rates of approximation of nonsmooth integral-type functionals of Markov processes by integral sums. Our approach is, in a sense, process insensitive and is…