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Diffusion approximation of nuclear space-valued stochastic differential equations driven by Poisson random measures. (English) Zbl 0845.60008

The authors consider a sequence of stochastic differential equations driven by Poisson random measures in the dual of a countable Hilbertian nuclear space. They derive sufficient conditions for the weak convergence of such a sequence to the solution of diffusion equation. Some applications to the models of environmental pollution and neuronal behavior are considered.

MSC:

60B10 Convergence of probability measures
60F05 Central limit and other weak theorems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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