Convergence of continuous stochastic processes on compact metric spaces converging in the Lipschitz distance

Kohei Suzuki

Convergence of continuous stochastic processes on compact metric spaces converging in the Lipschitz distance

Probability 2014-12-03 v1

Authors: Kohei Suzuki

Abstract

We introduce a new distance, a Lipschitz-Prokhorov distance $d_{LP}$ , on the set $\mathcal {PM}$ of isomorphism classes of pairs $(X, P)$ where $X$ is a compact metric space and $P$ is the law of a continuous stochastic process on $X$ . We show that $(\mathcal {PM}, d_{LP})$ is a complete metric space. For Markov processes on Riemannian manifolds, we study relative compactness and convergence.

Keywords

Lipschitz-Prokhorov distance continuous stochastic processes compact metric spaces convergence relative compactness Markov processes Riemannian manifolds

Cite

@article{arxiv.1412.0736,
  title  = {Convergence of continuous stochastic processes on compact metric spaces converging in the Lipschitz distance},
  author = {Kohei Suzuki},
  journal= {arXiv preprint arXiv:1412.0736},
  year   = {2014}
}

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29 pages, 1 figure

Convergence of continuous stochastic processes on compact metric spaces converging in the Lipschitz distance

Abstract

Keywords

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