Stochastic De Giorgi iteration and regularity of stochastic partial differential equations

• Elton P. Hsu ^[1] ; Yu Wang ^[3] ; Zhenan Wang ^[2]
  1. [1] Northwestern University

     Northwestern University

     Township of Evanston, Estados Unidos

     
  2. [2] University of Washington

     University of Washington

     Estados Unidos

     
  3. [3] Goldman Sachs (USA)

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 5, 2017, págs. 2855-2866
• Idioma: inglés
• DOI: 10.1214/16-AOP1126
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• Resumen

  • Under general conditions, we devise a stochastic version of De Giorgi iteration scheme for semilinear stochastic parabolic partial differential equation of the form ∂tu=div⁡(A∇u)+f(t,x,u)+gi(t,x,u)w˙ti with progressively measurable diffusion coefficients. We use the scheme to show that the solution of the equation is almost surely Hölder continuous in both space and time variables.