We define a two-parameter scale of Banach spaces contained in the contininuous functions on the space of probability measures on a compact metric space X, and show that the resolvent of the Fleming-Viot process is a bounded operator in the scale. We use this result to prove uniqueness of solutions to the martingale problem for Fleming-Viot operators whose mutation operator (Aμ, A) and sampling rate γ(μ, x, y) may depend on the measure variable μ ∈ M1(X), provided they are sufficiently close to constant in a sense made precise by the norms defining the scale. We prove an existence result with no such restriction on the coefficients.

Journal of Functional Analysis
School of Mathematics and Statistics

Dawson, D.A, & March, P. (1995). Resolvent Estimates for Fleming-Viot Operators and Uniqueness of Solutions to Related Martingale Problems. Journal of Functional Analysis, 132(2), 417–472. doi:10.1006/jfan.1995.1111