Zobrazeno 1 - 10
of 142
pro vyhledávání: '"Pavlyukevich, Ilya"'
Autor:
Pavlyukevich, Ilya, Pilipenko, Andrey
In this paper we study Markov chains with the state space given by the coordinate axes of $\mathbb R^m$, $m \geq 2$, whose step sizes on each positive half-axis are distributed according to a centered probability distribution with variance $v_i^2 \in
Externí odkaz:
http://arxiv.org/abs/2310.10809
In our paper [Bernoulli 26(2), 2020, 1381-1409], we found all strong Markov solutions that spend zero time at $0$ of the Stratonovich stochastic differential equation $d X=|X|^{\alpha}\circ dB$, $\alpha\in (0,1)$. These solutions have the form $X_t^\
Externí odkaz:
http://arxiv.org/abs/2308.06646
We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperplane interfaces with oblique penetration. We show that this system has
Externí odkaz:
http://arxiv.org/abs/2303.02740
In this paper we solve a L\'evy driven linear stochastic first order partial differential equation (transport equation) understood in the canonical (Marcus) form. The solution can be obtained with the help of the method of stochastic characteristics.
Externí odkaz:
http://arxiv.org/abs/2303.00674
Publikováno v:
Journal of Statistical Physics 2024
This article establishes explicit non-asymptotic ergodic bounds in the renormalized Wasserstein-Kantorovich-Rubinstein (WKR) distance for a viscous energy shell lattice model of turbulence with random energy injection. The system under consideration
Externí odkaz:
http://arxiv.org/abs/2302.13968
Publikováno v:
The Journal of Geometric Analysis volume 31, pages 12446--12484 (2021) (open access)
We show that geodesic random walks on a complete Finsler manifold of bounded geometry converge to a diffusion process which is, up to a drift, the Brownian motion corresponding to a Riemannian metric.
Comment: 32 pages, 3 figures. Comments from
Comment: 32 pages, 3 figures. Comments from
Externí odkaz:
http://arxiv.org/abs/2102.08296
Autor:
Kulik, Alexei, Pavlyukevich, Ilya
In this paper we show that if large jumps of an It\^o-semimartingale $X$ have a finite $p$-moment, $p>0$, the radial part of its drift is dominated by $-|X|^\kappa$ for some $\kappa\geq -1$, and the balance condition $p+\kappa>1$ holds true, then und
Externí odkaz:
http://arxiv.org/abs/2004.12449
Autor:
Pavlyukevich, Ilya, Pilipenko, Andrey
Let $A_\pm>0$, $\beta\in(0,1)$, and let $Z^{(\alpha)}$ be a strictly $\alpha$-stable L\'evy process with the jump measure $\nu(\mathrm{d} z)=(C_+\mathbb{I}_{(0,\infty)}(z)+ C_-\mathbb{I}_{(-\infty,0)}(z))|z|^{-1-\alpha}\,\mathrm{d} z$, $\alpha\in (1,
Externí odkaz:
http://arxiv.org/abs/2004.05421
For solutions $X=(X_t)_{t\in[0,T]}$ of L\'evy-driven Marcus stochastic differential equations we study the Wong--Zakai type time discrete approximations $\bar X=(\bar X_{kh})_{0\leq k\leq T/h}$, $h>0$, and establish the first order convergence $|E f(
Externí odkaz:
http://arxiv.org/abs/2002.02652
We consider the problem of estimation of the drift parameter of an ergodic Ornstein--Uhlenbeck type process driven by a L\'evy process with heavy tails. The process is observed continuously on a long time interval $[0,T]$, $T\to\infty$. We prove that
Externí odkaz:
http://arxiv.org/abs/1911.11202