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SDDEs limits solutions to sublinear reaction-diffusion SPDEs. (English) Zbl 1035.60065

The author introduces a new definition of solutions to heat-based stochastic partial differential equations (SPDE) driven by space-time white noise, namely “stochastic differential-difference equations (SDDE) limits solutions”. In particular he treats one-spatial-dimensional reaction-diffusion stochastic partial differential equations and, assuming Hölder coefficients, he proves weak existence, uniqueness in law, regularity and dependence on the coefficients.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
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