Exponential convergence in the Wasserstein metric W₁ for one dimensional diffusions

2017/03/01 by Cheng, Lingyan, Li, Ruinan, Wu, Liming
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1703.00507

Abstract

In this paper, we find some general and efficient sufficient conditions for the exponential convergence W_1,d(P_t(x,⋅), P_t(y,⋅) )≤ Ke^-δtd(x,y) for the semigroup (P_t) of one-dimensional diffusion. Moreover some sharp estimates of the involved constants K≥ 1, δ>0 are provided. Those general results are illustrated by a series of examples.

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