Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises

Dejun Luo and Jian Wang

Stochastic Processes and their Applications, 2019, vol. 129, issue 9, 3129-3173

Abstract: We establish the exponential convergence with respect to the L1-Wasserstein distance and the total variation for the semigroup corresponding to the stochastic differential equation dXt=dZt+b(Xt)dt,where (Zt)t≥0 is a pure jump Lévy process whose Lévy measure ν fulfills infx∈Rd,|x|≤κ0[ν∧(δx∗ν)](Rd)>0for some constant κ0>0, and the drift term b satisfies that for any x,y∈Rd, 〈b(x)−b(y),x−y〉≤Φ1(|x−y|)|x−y|,|x−y|Keywords: Refined basic coupling; Lévy jump process; Wasserstein-type distance; Strong ergodicity (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.09.003

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