40 citations · 69 across the 16 of their papers we have counts for
11 papers · 1 filter
Geometric ergodicity of modified Euler schemes for SDEs with super-linearity
Jianhai Bao, Mateusz B. Majka, Jian Wang
As a well-known fact, the classical Euler scheme works merely for SDEs with coefficients of linear growth. In this paper, we study a general framework of modified Euler schemes, wh…
-Wasserstein contraction for Euler schemes of elliptic diffusions and interacting particle systems
Linshan Liu, Mateusz B. Majka, Pierre Monmarché
We show the -Wasserstein contraction for the transition kernel of a discretised diffusion process, under a contractivity at infinity condition on the drift and a sufficiently…
Optimal Markovian coupling for finite activity Lévy processes
Wilfrid S. Kendall, Mateusz B. Majka, Aleksandar Mijatović
We study optimal Markovian couplings of Markov processes, where the optimality is understood in terms of minimization of concave transport costs between the time-marginal distribut…
Strict Kantorovich contractions for Markov chains and Euler schemes with general noise
Lu-Jing Huang, Mateusz B. Majka, Jian Wang
We study contractions of Markov chains on general metric spaces with respect to some carefully designed distance-like functions, which are comparable to the total variation and the…
Approximation of heavy-tailed distributions via stable-driven SDEs
Lu-Jing Huang, Mateusz B. Majka, Jian Wang
Constructions of numerous approximate sampling algorithms are based on the well-known fact that certain Gibbs measures are stationary distributions of ergodic stochastic differenti…
Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise
Mingjie Liang, Mateusz B. Majka, Jian Wang
We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump Lévy processes. We prove a uniform in time propag…
Quantitative contraction rates for Markov chains on general state spaces
Andreas Eberle, Mateusz B. Majka
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ( Wasserstein) distances. For diffusion processes, relatively pr…
Non-asymptotic bounds for sampling algorithms without log-concavity
Mateusz B. Majka, Aleksandar Mijatović, Lukasz Szpruch
Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-a…
A note on existence of global solutions and invariant measures for jump SDEs with locally one-sided Lipschitz drift
Mateusz B. Majka
We extend some methods developed by Albeverio, Brzeźniak and Wu and we show how to apply them in order to prove existence of global strong solutions of stochastic differential equa…
Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling
Mateusz B. Majka
By using the mirror coupling for solutions of SDEs driven by pure jump Lévy processes, we extend some transportation and concentration inequalities, which were previously known onl…
Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes
Mateusz B. Majka
We present a novel idea for a coupling of solutions of stochastic differential equations driven by Lévy noise, inspired by some results from the optimal transportation theory. Then…