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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…
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…