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Research Article Open access CC BY 4.0

Weak Moment of a Class of Stochastic Heat Equation with Martingale-valued Harmonic Function

Ejighikeme McSylvester Omaba

Asian Research Journal of Mathematics · pp. 1–16 · Published 15 Mar 2017

10.9734/ARJOM/2017/31665

Abstract

A study of a non-linear parabolic SPDEs of the form with  as the space-time white noise and a space-time harmonic function was done. The function  is Lipschitz continuous and  the  -generator of a Lévy process . Some precise condition for existence and uniqueness of the solution were given and we show that the solution grows weakly(in law/distribution) in time (for large ) at most a precise exponential rate for the  ; and grows in time at most a precise exponential rate for the case of  generator of an alpha-stable process .

Stochastic heat equations (she) space-time harmonic function hitting time Hermite polynomials Doob’s maximal inequality

References (8)

  1. 1 Brownian Motion and Stochastic Calculus [DOI]
  2. 2 Geometric Theory of Semilinear Parabolic Equations [DOI]
  3. 3 An introduction to stochastic partial differential equations [DOI]
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  6. 6 On nonexistence of global solutions for some nonlinear integral equations [DOI]
  7. 7 Nonlinear noise excitation of intermittent stochastic PDEs and the topology of LCA groups [DOI]
  8. 8 Some Properties of a class of stochastic heat equations

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