Stochastic viscosity solutions for nonlinear stochastic partial di # erential equations . Part I

@inproceedings{Buckdahna2001StochasticVS,
  title={Stochastic viscosity solutions for nonlinear stochastic partial di # erential equations . Part I},
  author={Rainer Buckdahna and Jin Mab},
  year={2001}
}
  • Rainer Buckdahna, Jin Mab
  • Published 2001
This paper, together with the accompanying work (Part II, Stochastic Process. Appl. 93 (2001) 205–228) is an attempt to extend the notion of viscosity solution to nonlinear stochastic partial di#erential equations. We introduce a de7nition of stochastic viscosity solution in the spirit of its deterministic counterpart, with special consideration given to the stochastic integrals. We show that a stochastic PDE can be converted to a PDE with random coe9cients via a Doss–Sussmann-type… CONTINUE READING
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