Stochastic reaction-diffusion equations driven by jump processes

Zdzislaw Brzezniak; Erika Hausenblas; Paul Razafimandimby

doi:10.1007/s11118-017-9651-9

Stochastic reaction-diffusion equations driven by jump processes

Zdzislaw Brzezniak, Erika Hausenblas, Paul Razafimandimby

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.

Original language	English
Pages (from-to)	131-201
Number of pages	71
Journal	Potential analysis
Volume	49
Early online date	21 Sept 2017
DOIs	https://doi.org/10.1007/s11118-017-9651-9
Publication status	Published - Jul 2018

Bibliographical note

Keywords

It\^o integral driven by a Poisson random measure
stochastic partial differential equations
L\'evy processes
Reaction Diffusion Equations

Access to Document

10.1007/s11118-017-9651-9Licence: Unspecified

BrzHausRaz_ 02Sept2017_new
© The Author(s) 2017.
Accepted author manuscript, 302 KBLicence: Unspecified

Cite this

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title = "Stochastic reaction-diffusion equations driven by jump processes",

abstract = "We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.",

keywords = "It\^o integral driven by a Poisson random measure, stochastic partial differential equations, L\'evy processes, Reaction Diffusion Equations",

author = "Zdzislaw Brzezniak and Erika Hausenblas and Paul Razafimandimby",

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AU - Hausenblas, Erika

AU - Razafimandimby, Paul

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N2 - We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.

AB - We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.

KW - It\^o integral driven by a Poisson random measure

KW - stochastic partial differential equations

KW - L\'evy processes

KW - Reaction Diffusion Equations

U2 - 10.1007/s11118-017-9651-9

DO - 10.1007/s11118-017-9651-9

M3 - Article

SN - 0926-2601

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JO - Potential analysis

JF - Potential analysis

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