Countable Systems of Degenerate Stochastic Differential Equations with Applications to Super-Markov Chains
Richard F Bass, University of Connecticut, USA
Edwin A. Perkins, The University of British Columbia
Abstract
We prove well-posedness of the martingale problem for an
infinite-dimensional degenerate
elliptic operator under appropriate Hölder continuity conditions on
the
coefficients. These martingale problems include large population
limits of
branching particle systems on a countable state space in which the
particle
dynamics and branching rates may depend on the entire population in a
Hölder
fashion. This extends an approach originally used by the authors in
finite
dimensions.
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