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Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values

by A. Andersson and A. Jentzen and R. Kurniawan

(Report number 2015-47)

Abstract
In this article we develop a framework for studying parabolic semilinear stochastic evolution equations (SEEs) with singularities in the initial condition and singularities at the initial time of the time-dependent coefficients of the considered SEE. We use this framework to establish existence, uniqueness, and regularity results for mild solutions of parabolic semilinear SEEs with singularities at the initial time. We also provide several counterexample SEEs that illustrate the optimality of our results.

Keywords: Stochastic evolution equations

@Techreport{AJK15_637,
  author = {A. Andersson and A. Jentzen and R. Kurniawan},
  title = {Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-47},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-47.pdf },
  year = {2015}
}

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