The parametrix method for parabolic SPDEs

Andrea Pascucci and Antonello Pesce

Stochastic Processes and their Applications, 2020, vol. 130, issue 10, 6226-6245

Abstract: We consider the Cauchy problem for a linear stochastic partial differential equation. By extending the parametrix method for PDEs whose coefficients are only measurable with respect to the time variable, we prove existence, regularity in Hölder classes and estimates from above and below of the fundamental solution. This result is applied to SPDEs by means of the Itô–Wentzell formula, through a random change of variables which transforms the SPDE into a PDE with random coefficients.

Keywords: Stochastic partial differential equations; Fundamental solution; Parametrix method; Kolmogorov equation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2020.05.008

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