Global martingale solutions for a stochastic population cross-diffusion system

Gaurav Dhariwal, Ansgar Jüngel and Nicola Zamponi

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 3792-3820

Abstract: 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 Brzeźniak 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.

Keywords: Shigesada–Kawasaki–Teramoto model; Population dynamics; Martingale solutions; Tightness; Skorokhod–Jakubowski theorem; Stochastic maximum principle (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2018.11.001

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