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Exponential convergence in the Wasserstein metric $W_1$ for one dimensional diffusions
Lingyan Cheng, Ruinan Li, Liming Wu · 2017-03-02 · via math.PR updates on arXiv.org

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

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