Moment bounds for a class of fractional stochastic heat equations

2014/09/19 by Mohammud Foondun, Wei Liu, Foondun, Mohammud +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1409.5687

openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider fractional stochastic heat equations of the form (∂ u_t(x))/(∂ t) = -(-Δ)^α/2 u_t(x)+λσ(u_t(x)) F(t, x). Here F denotes the noise term. Under suitable assumptions, we show that the second moment of the solution grows exponentially with time. In particular, this answers an open problem in \citeCoKh. Along the way, we prove a number of other interesting properties which extend and complement results in \citefoonjose, \citeKhoshnevisan:2013aa and \citeKhoshnevisan:2013ab.

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