Transition probabilities for degenerate diffusions arising in population genetics

• 成果类型: Article
• 署名作者: Epstein, Charles L.; Pop, Camelia A.
• 署名单位: University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0840-2
• 发表日期: 2019
• 页码: 537-603
• 关键词: harnack inequality; uniqueness; EQUATIONS

摘要

We provide a detailed description of the structure of the transition probabilities and of the hitting distributions on 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.