Weak Moment of a Class of Stochastic Heat Equation with Martingale-valued Harmonic Function
Ejighikeme Mcsylvester Omaba *
Department of Mathematics, Computer Science, Statistics and Informatics, Faculty of Science, Federal University, Ndufu-Alike Ikwo, P.M.B 1010, Abakaliki, Ebonyi State, Nigeria
*Author to whom correspondence should be addressed.
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 .
Keywords: Stochastic heat equations (she), space-time harmonic function, hitting time, Hermite polynomials, Doob’s maximal inequality