Exponential convergence in the Wasserstein metric $W_1$ for one dimensional diffusions

Lingyan Cheng; Ruinan Li; Liming Wu

Exponential convergence in the Wasserstein metric $W_1$ for one dimensional diffusions

Probability 2017-03-03 v1

Authors: Lingyan Cheng , Ruinan Li , Liming Wu

Abstract

In this paper, we find some general and efficient sufficient conditions for the exponential convergence $W_{1,d}(P_t(x,\cdot), P_t(y,\cdot) )\le Ke^{-\delta t}d(x,y)$ for the semigroup $(P_t)$ of one-dimensional diffusion. Moreover some sharp estimates of the involved constants $K\ge 1, \delta>0$ are provided. Those general results are illustrated by a series of examples.

Keywords

wasserstein distance diffusion processes random matrix ensembles

Cite

@article{arxiv.1703.00507,
  title  = {Exponential convergence in the Wasserstein metric $W_1$ for one dimensional diffusions},
  author = {Lingyan Cheng and Ruinan Li and Liming Wu},
  journal= {arXiv preprint arXiv:1703.00507},
  year   = {2017}
}

Comments

18 pages

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