Summary
An existence theorem in the spirit of Keisler [Ke], is proved for the simple one-dimensional diffusion equation driven by white noise modulated by a non-linear function of the solution. This is used to obtain a density and a Stochastic Partial Differential Equation in one dimension for the critical branching diffusion studied by Dawson et al.
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This research was carried out while the author was at the Department of Mathematics, University of British Columbia
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Reimers, M. One dimensional stochastic partial differential equations and the branching measure diffusion. Probab. Th. Rel. Fields 81, 319–340 (1989). https://doi.org/10.1007/BF00340057
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DOI: https://doi.org/10.1007/BF00340057