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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.

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