Analysis of Infinite-dimensional Markovian Models

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We performed this project and obtained the following results. 1. Fleming-Viot proccesess form an important class of measure-valued Markov processes and well-applied as basic models to population genetics. Concerning these we resolved an open problem to determine the situation that the Fleming-Viot processes have time reversible stationary distribution. 2. In the case that selective intensity is unbounded we proved well-posedness of the processes and uniqueness of stationary distribution. This problem is much harder than the bounded selection case. 3. Interacting diffusion systems form an important class of the theory of interacting Markov processes, which have been well developed when the noises are spatially independent. We considered spatially correlated noises, and obtained some ergodic results. 4. Heat equation with Gausian white noise potential defines a function-valued diffusion, which is important from a view point of random polymer model. For this equation we developed asymptotic analysis of moments of the solution.