A. Kulik

activity

20092021

most citedTOI-1842b: A Transiting Warm Saturn Undergoing Re-Inflation around an Evolving Subgiant

18 citations · 43 across the 23 of their papers we have counts for

collaborators

29 papers

astro-ph.EP2021★ 18 cited

TOI-1842b: A Transiting Warm Saturn Undergoing Re-Inflation around an Evolving Subgiant

Robert A. Wittenmyer, Jake T. Clark, Trifon Trifonov +41

The imminent launch of space telescopes designed to probe the atmospheres of exoplanets has prompted new efforts to prioritise the thousands of transiting planet candidates for fol…

math.PR2021★ 1 cited

On weak solution of SDE driven by inhomogeneous singular Lévy noise

Tadeusz Kulczycki, Alexei Kulik, Michał Ryznar

We study a time-inhomogeneous SDE in $R^{d}$ driven by a cylindrical Lévy process with independent coordinates which may have different scaling properties. Such a structure of the d…

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★ 1 cited

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…

math.PR2018

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…

math.PR2018

Approximation in law of locally $α$ -stable Lévy-type processes by non-linear regressions

Alexei Kulik

We study a real-valued Lévy-type process $X$ , which is locally $α$ -stable in the sense that its jump kernel is a combination of a `principal' (state dependent) $α$ -stable part with…

math.PR2018★ 1 cited

Generalized couplings and ergodic rates for SPDEs and other Markov models

Oleg Butkovsky, Alexei Kulik, Michael Scheutzow

We establish verifiable general sufficient conditions for exponential or subexponential ergodicity of Markov processes that may lack the strong Feller property. We apply the obtain…

math.PR2017

Non-Gaussian Limit Theorem for Non-Linear Langevin Equations Driven by Lévy Noise

Alexei Kulik, Ilya Pavlyukevich

In this paper, we study the small noise behaviour of solutions of a non-linear second order Langevin equation $\ddot x^\varepsilon_t +|\dot x^\varepsilon_t|^β=\dot Z^\varepsilon_{\…

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★ 2 cited

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.PR2016★ 1 cited

Generalized couplings and convergence of transition probabilities

Alexei Kulik, Michael Scheutzow

We provide sufficient conditions for the uniqueness of an invariant measure of a Markov process as well as for the weak convergence of transition probabilities to the invariant mea…

math.PR2015★ 2 cited

On weak uniqueness and distributional properties of a solution to an SDE with $α$ -stable noise

Alexei Kulik

For an SDE driven by a rotationally invariant $α$ -stable noise we prove weak uniqueness of the solution under the balance condition $α + γ > 1$ , where $γ$ denotes the Holder index of t…

math.PR2015★ 1 cited

Weak approximation rates for integral functionals of Markov processes

Iurii Ganychenko, Alexei Kulik

We obtain weak rates for approximation of an integral functional of a Markov process by integral sums. An assumption on the process is formulated only in terms of its transition pr…

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…

math.PR2014★ 1 cited

Parametrix construction of the transition probability density of the solution to an SDE driven by $α$ -stable noise

Victoria Knopova, Alexei Kulik

Let $L := - a (x) (- Δ)^{α /2} + (b (x), \nabla)$ , where $α \in (0, 2)$ , and $a:\rd\to (0,\infty)$, $b: \rd\to \rd$. Under certain regularity assumptions on the coefficients $a$ and $b$ , we…

math.PR2014

A coupling approach to Doob's theorem

Alexei Kulik, Michael Scheutzow

We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $μ$ converge to $μ…

math.PR2013

Lift zonoid order and functional inequalities

Alexei M. Kulik, Taras D. Tymoshkevych

We introduce the notion of a weighted lift zonoid and show that, for properly chosen weights v, the ordering condition on a measure μ, formulated in terms of the weighted lift zono…

math.PR2013

Intrinsic compound kernel estimates for the transition probability density of a Lévy type processes and their applications

Victoria P. Knopova, Alexei M. Kulik

In this paper we construct the fundamental solution to some integro-differential equation, as well as the intrinsic upper and lower estimates for this solution. As an application o…

math.PR2013

Parametrix construction for certain Lévy-type processes

Victoria Knopova, Alexei Kulik

In this paper we show that a non-local operator of certain type extends to the generator of a strong Markov process, admitting the transition probability density. For this transiti…

TOI-1842b: A Transiting Warm Saturn Undergoing Re-Inflation around an Evolving Subgiant

On weak solution of SDE driven by inhomogeneous singular Lévy noise

On regularization by a small noise of multidimensional ODEs with non-Lipschitz coefficients

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

Construction and heat kernel estimates of general stable-like Markov processes

Moment bounds for dissipative semimartingales with heavy jumps

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

Well-Posedness, Stability, and Sensitivities for Stochastic Delay Equations: A Generalized Coupling Approach

Approximation in law of locally α-stable Lévy-type processes by non-linear regressions

Generalized couplings and ergodic rates for SPDEs and other Markov models

Non-Gaussian Limit Theorem for Non-Linear Langevin Equations Driven by Lévy Noise

Large deviation principle for one-dimensional SDEs with discontinuous coefficients

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

Long time behavior of stochastic hard ball systems

Generalized couplings and convergence of transition probabilities

On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise

Weak approximation rates for integral functionals of Markov processes

A martingale bound for the entropy associated with a trimmed filtration on Rd

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

Parametrix construction of the transition probability density of the solution to an SDE driven by α-stable noise

A coupling approach to Doob's theorem

Lift zonoid order and functional inequalities

Intrinsic compound kernel estimates for the transition probability density of a Lévy type processes and their applications

Parametrix construction for certain Lévy-type processes

Approximation in law of locally $α$ -stable Lévy-type processes by non-linear regressions

On weak uniqueness and distributional properties of a solution to an SDE with $α$ -stable noise

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

Parametrix construction of the transition probability density of the solution to an SDE driven by $α$ -stable noise