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Local times for superprocesses
Abstract
Measure-valued random processes arise in a variety of situations, both pure and applied. In recent years there has been much interest in a class of measure-valued Markov processes known as superprocesses. These occur as high-density limits of branching and diffusing particle systems, and as solutions to measure-valued martingale problems and stochastic PDEs. In this work, we study local times for superprocesses. We begin by deriving analogues of well-known properties of ordinary local times. Then, restricting our attention to a particular class of superprocesses (which includes the important case of super-Brownian motion), we prove more detailed properties of the local times, such as joint continuity and a global Holder condition. These are then used to investigate path properties of the superprocesses themselves. For example, we give a lower bound on the Hausdorff dimension of the "level sets" of the superprocess. The proofs of some of the main results are based on a detailed analysis of product moments of the local times.
Subject Area
Mathematics
Recommended Citation
Krone, Stephen Michael, "Local times for superprocesses" (1990). Doctoral Dissertations Available from Proquest. AAI9100518.
https://scholarworks.umass.edu/dissertations/AAI9100518