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Stochastic partial differential equations for a class of interacting measure-valued diffusions. (English) Zbl 0973.60077
There are investigated interacting branching measure-valued diffusions (IBMDs), which are solutions to the well-posed martingale problem. A new class of stochastic partial differential equations (based on two orthogonal \({\mathcal S}'(R)\)-valued cylindrical Brownian motions) for the density process associated with such IBMDs (when these densities exist) is introduced.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
60G57 Random measures
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