标题： 雅可比过程的狄利克雷型分析 显示英文标题

标题： Dirichlet form analysis of the Jacobi process

摘要： 我们利用狄利克雷形式构造并分析雅可比过程——在数学生物学中称为沃伊特-费舍尔扩散——。相应的狄利克雷空间具有不同权重的索伯列夫空间形式，分别用于函数本身及其导数。根据参数，我们描述狄利克雷空间中函数的边界行为，展示密度结果，推导索伯列夫嵌入，并验证硬y型的函数不等式。由于生成元是一个超几何微分算子，许多证明可以通过涉及超几何函数的显式计算来完成。我们推导出相关半群和马尔可夫过程的相应性质，并表明后者在一些小的技术修改下是雅可比随机微分方程的解。 显示英文摘要

摘要： We construct and analyze the Jacobi process - in mathematical biology referred to as Wright-Fisher diffusion - using a Dirichlet form. The corresponding Dirichlet space takes the form of a Sobolev space with different weights for the function itself and its derivative. Depending on the parameters we characterize the boundary behavior of the functions in the Dirichlet space, show density results, derive Sobolev embeddings and verify functional inequalities of Hardy type. Since the generator is a hypergeometric differential operator, many of the proofs can be carried out by explicit calculations involving hypergeometric functions. We deduce corresponding properties for the associated semigroup and Markov process and show that the latter is up to minor technical modifications a solution to the Jacobi SDE.