Generalized space-time fractional stochastic kinetic equation

2022/01/17 by Junfeng Liu, Liu, Junfeng
Economics, Econometrics and Finance · Mathematics · #60G22 #60H07 #60H15 #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2201.06345

openalex publication_date 2022/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in ℝ^d with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the non-linear stochastic heat equation involving fractional derivative in time and fractional Laplacian in space. We give a necessary condition on the spatial covariance for the existence and uniqueness of the solution. We also study various properties of the solution: path regularity, the behavior of second moment and the stationarity in the case of linear additive noise.

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