Long-term behavior for superprocesses over a stochastic flow.
Local extinction for superprocesses in random environments.
Large deviations and quasi-potential of a Fleming-Viot process.
Nonlinear filtering with signal dependent observation noise.
Nonlinear filtering for reflecting diffusions in random environments via nonparametric estimation.
Mutually catalytic branching in the plane: Infinite measure states.
Some properties of superprocesses under a stochastic flow
For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s -theory for linear SPDE.
Mutually catalytic branching in the plane : uniqueness
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