A certain class of infinite dimensional diffusion processes arising in population genetics
A certain class of infinite dimensional diffusion processes arising in population genetics
Let $S$ be a countable set, and let $X= \{x=(x_{i})_{i\in S} : x_{i}\geqq 0(i\in S),\sum_{i\in S}x_{i}=1\}$ be the totality of probability vectors on $S$ , which is equipped with the weak topology.Suppose that we are given a second order differential operator $L$ of the following type: (1.1) $L= \frac{1}{2}\sum_{i\in S}\sum_{j\in …