Analyticity of a class of degenerate evolution equations on the canonical simplex of $\R^d$ arising from Fleming--Viot processes

TL;DR

This paper investigates the analyticity of semigroups generated by degenerate second order differential operators linked to Fleming--Viot processes on the canonical simplex, enhancing understanding of their mathematical properties.

Contribution

It establishes the analyticity of these semigroups in the context of population genetics models, providing new insights into their mathematical structure.

Findings

Proves semigroup analyticity for a class of degenerate operators

Connects operator properties to Fleming--Viot processes

Advances theoretical understanding of population genetics models

Abstract

We study the analyticity of the semigroups generated by a class of degenerate second order differential operators in the space $C(S_d)$, where $S_d$ is the canonical simplex of $\R^d$. The semigroups arise from the theory of Fleming--Viot processes in population genetics.