Hölder continuity of the solutions to a class of SPDE’s arising from branching particle systems in a random environment

Hu, Yaozhong, Nualart, David and Xia, Panqiu 2019. Hölder continuity of the solutions to a class of SPDE’s arising from branching particle systems in a random environment. Electronic Journal of Probability 24 , pp. 1-52. 10.1214/19-ejp357

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Abstract

We consider a d-dimensional branching particle system in a random environment. Suppose that the initial measures converge weakly to a measure with bounded density. Under the Mytnik-Sturm branching mechanism, we prove that the corresponding empirical measure Xnt converges weakly in the Skorohod space D([0,T];MF(Rd)) and the limit has a density ut(x), where MF(Rd) is the space of finite measures on Rd. We also derive a stochastic partial differential equation ut(x) satisfies. By using the techniques of Malliavin calculus, we prove that ut(x) is jointly Hölder continuous in time with exponent 12−ϵ and in space with exponent 1−ϵ for any ϵ>0.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Institute of Mathematical Statistics
ISSN:	1083-6489
Date of First Compliant Deposit:	1 August 2024
Date of Acceptance:	8 September 2019
Last Modified:	18 Sep 2024 10:45
URI:	https://orca.cardiff.ac.uk/id/eprint/171075

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