Solution theory to semilinear parabolic stochastic partial differential equations with polynomially bounded coefficients

2020/10/14 by Alessia Ascanelli, Ascanelli, Alessia, Sandro Coriasco +3
Computer Science · Economics, Econometrics and Finance · Engineering · #35L10 #60H15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2010.07087

openalex publication_date 2020/10/14 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide conditions on the initial data and on the stochastic terms, namely, on the associated spectral measure, so that these mild solutions exist uniquely in suitably chosen functional classes.

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