### 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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Pages: 634-673

Publication Date: October 6, 2004

DOI: 10.1214/EJP.v9-222

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