Transition probabilities for degenerate diffusions arising in population genetics

Charles L. Epstein; Camelia A. Pop

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arXiv · 1608.02119

Transition probabilities for degenerate diffusions arising in population genetics

Charles L. Epstein·Camelia A. Pop

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Abstract

We provide a detailed description of the structure of the transition probabilities and of the hitting distributions of boundary components of a manifold with corners for a degenerate strong Markov process arising in population genetics. The Markov processes that we study are a generalization of the classical Wright-Fisher process. The main ingredients in our proofs are based on the analysis of the regularity properties of solutions to a forward Kolmogorov equation defined on a compact manifold with corners, which is degenerate in the sense that it is not strictly elliptic and the coefficients of the first order drift term have mild logarithmic singularities.

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Charles L. Epstein, Camelia A. Pop. 2016-08-06. Transition probabilities for degenerate diffusions arising in population genetics. https://arxiv.org/abs/1608.02119

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