We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. Both linear and semilinear equations are considered, under suitable hyperbolicity hypotheses on the linear part. We provide conditions on the initial data and on the stochastic terms, namely, on the associated spectral measure, so that mild solutions exist and are unique in suitably chosen functional classes. In the linear case, random field solutions are obtained, while in the semilinear case we study function-valued solutions. In both situations, a regularity result on the expectation value of the solution is obtained.
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|Titolo:||Solution theory to hyperbolic stochastic partial differential equations with polynomially bounded coefficients|
|Data di pubblicazione:||2016|
|Appare nelle tipologie:||08.6 Working Paper|