A Class of Infinite-Dimensional Diffusion Processes with Connection to Population Genetics
Shui Feng, Feng‐Yu Wang · Journal of Applied Probability · 2007
Starting from a sequence of independent Wright-Fisher diffusion processes on [0, 1], we construct a class of reversible infinite-dimensional diffusion processes on Δ∞:= {x∈ [0, 1]N: ∑i≥1xi= 1} with GEM distribution as the reversible measure. Log-Sobolev inequalities are established for these diffusions, which lead to the exponential convergence of the corresponding reversible measures in the entropy. Extensions are made to a class of measure-valued processes over an abstract spaceS. This provides a reasonable alternative to the Fleming-Viot process, which does not satisfy the log-Sobolev inequality whenSis infinite as observed by Stannat (2000).