arXiv subjects
Publications and source records attributed to Byron Schmuland.
Reversibility of the Fleming-Viot process with mutation, selection, and recombination is well understood. In this paper, we study the reversibility of a system of Fleming-Viot processes that live on a countable number of colonies interacting with each other through migrations between the colonies. It is shown that reversibility fails when both migration and mutation are non-trivial.
Skew convolution semigroups play an important role in the study of generalized Mehler semigroups and Ornstein-Uhlenbeck processes. We give a characterization for a general skew convolution semigroup on real separable Hilbert space whose characteristic functional is not necessarily differentiable at the initial time. A connection between this subject and catalytic branching superprocesses is established through fluctuation limits, providing a rich class of non-differentiable skew convolution semigroups. Path regularity of the corresponding generalized Ornstein-Uhlenbeck processes in different topologies is also discussed.
The Dirichlet form associated with the intrinsic gradient on Poisson space is known to be quasi-regular on the complete metric space $\ddotΓ=$ $\{Z_+$-valued Radon measures on $\IR^d\}$. We show that under mild conditions, the set $\ddotΓ\setminusΓ$ is $\e$-exceptional, where $Γ$ is the space of locally finite configurations in $\IR^d$, that is, measures $γ\in\ddotΓ$ satisfying $\sup_{x\in\IR^d}γ(\{x\})\leq 1$. Thus, the associated diffusion lives on the smaller space $Γ$. This result also holds for Gibbs measures with superstable interactions.