Global martingale solutions for a stochastic population cross-diffusion system

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Dhariwal, Gaurav¹  Juengel, Ansgar¹  Zamponi, Nicola¹ 

[1] Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

关键词: Shigesada-Kawasaki-Teramoto model;    Population dynamics;    Martingale solutions;    Tightness;    Skorokhod-Jakubowski theorem;    Stochastic maximum principle;   

DOI  :  10.1016/j.spa.2018.11.001

来源: Elsevier

【 摘 要 】

The existence of global nonnegative martingale solutions to a stochastic cross-diffusion system for an arbitrary but finite number of interacting population species is shown. The random influence of the environment is modeled by a multiplicative noise term. The diffusion matrix is generally neither symmetric nor positive definite, but it possesses a quadratic entropy structure. This structure allows us to work in a Hilbert space framework and to apply a stochastic Galerkin method. The existence proof is based on energy-type estimates, the tightness criterion of Brzezniak and co-workers, and Jakubowski's generalization of the Skorokhod theorem. The nonnegativity is proved by an extension of Stampacchia's truncation method due to Chekroun, Park, and Temam. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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