โ Scribed by F.E. Benth; T. Deck; J. Potthoff
No coin nor oath required. For personal study only.
Cauchy problems for a class of non-linear stochastic evolution equations are studied. They are formulated as integral equations for generalized random fields. By methods of white noise analysis (S-transformation, characterization theorem, etc.) these problems are reduced to fixed point problems in appropriatly constructed Banach spaces. This technique provides a systematic treatment of existence and uniqueness questions for a variety of equations. The method is applied to non-linear heat equations, non-linear Volterra equations and non-linear ordinary differential equations, which may all be anticipating. For each case examples are given, such as the stochastic Burgers equation and stochastic reaction diffusion equations.
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