The inhomogeneous fractional stochastic heat equation driven by fractional Brownian motion

2024/04/18 by Rasha Alessa, R. Al Subaie, Alessa, R. +7
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2404.12088

openalex publication_date 2024/04/18 · openalex created_date 2024/04/20 · openalex updated_date 2026/07/28

Abstract

We investigate the fractional Hardy-Hénon equation with fractional Brownian noise ∂_tu(t)+(-Δ)^θ/2 u(t)=|x|^-γ |u(t)|^p-1u(t)+μ ∂_t B^H(t), where θ>0, p>1, γ≥ 0, μ∈ℝ, and the random forcing B^H is the fractional Brownian motion defined on some complete probability space (Ω, F, ℙ) with Hurst parameter H∈ (0,1). We establish the local existence and uniqueness of mild solutions under appropriate conditions on the parameters of the equation.

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