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

2014/12/01 by Suzuki, Kohei
#FOS: Mathematics #Primary 60F17 #Probability (math.PR) #Secondary 53C23

paper · doi:10.48550/arxiv.1412.0736

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.

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