A stochastic log-Laplace equation

• Jie Xiong ^[1]
  1. [1] University of Tennessee
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 3, 2, 2004, págs. 2362-2388
• Idioma: inglés
• DOI: 10.1214/009117904000000540
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• Resumen

  • We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term and making use of the particle system representation developed by Kurtz and Xiong [Stochastic Process. Appl. 83 (1999) 103–126]. We also derive the Wong–Zakai type approximation for this equation. As an application, we give a direct proof of the moment formulas of Skoulakis and Adler [Ann. Appl. Probab. 11 (2001) 488–543].