Markov uniqueness and Fokker-Planck-Kolmogorov equations

2021/09/18 by Sergio Albeverion, Albeverion, Sergio, В. И. Богачев +3
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2109.08883

Abstract

In this paper we show that Markov uniqueness for symmetric pre-Dirichlet operators L follows from the uniqueness of the corresponding Fokker-Planck-Kolmogorov equation (FPKE). Since in recent years a considerable number of uniqueness results for FPKE's have been achieved, we obtain new Markov uniqueness results in concrete cases. A selection of such will be presented in this paper. They include cases with killing and with degenerate diffusion coefficients.

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