INVARIANT MEASURES FOR SDES DRIVEN BY LEVY NOISE: A CASE STUDY FOR DISSIPATIVE NONLINEAR DRIFT IN INFINITE DIMENSION

S Albeverio; L Di Persio; E Mastrogiacomo; Boubaker Abdelhafid Omar Smii

INVARIANT MEASURES FOR SDES DRIVEN BY LEVY NOISE: A CASE STUDY FOR DISSIPATIVE NONLINEAR DRIFT IN INFINITE DIMENSION

S Albeverio, L Di Persio, E Mastrogiacomo, Boubaker Abdelhafid Omar Smii

Department of Mathematics

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

6 Scopus citations

Abstract

We study a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Levy noise. We define a Hilbert-Banach setting in which we prove existence and uniqueness of solutions under general assumptions on the drift and the Levy noise. We then prove a decomposition of the solution process into a stationary component, the law of which is identified with the unique invariant probability measure mu of the process, and a component which vanishes asymptotically for large times in the L-P (mu)-sense, for all 1 <= p < + infinity.

Original language	English
Journal	Communications in Mathematical Sciences
State	Published - 2017

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@article{de983a2786034234972405807dec7bdb,

title = "INVARIANT MEASURES FOR SDES DRIVEN BY LEVY NOISE: A CASE STUDY FOR DISSIPATIVE NONLINEAR DRIFT IN INFINITE DIMENSION",

abstract = "We study a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Levy noise. We define a Hilbert-Banach setting in which we prove existence and uniqueness of solutions under general assumptions on the drift and the Levy noise. We then prove a decomposition of the solution process into a stationary component, the law of which is identified with the unique invariant probability measure mu of the process, and a component which vanishes asymptotically for large times in the L-P (mu)-sense, for all 1 <= p < + infinity.",

author = "S Albeverio and \{Di Persio\}, L and E Mastrogiacomo and Smii, \{Boubaker Abdelhafid Omar\}",

year = "2017",

language = "English",

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TY - JOUR

T1 - INVARIANT MEASURES FOR SDES DRIVEN BY LEVY NOISE: A CASE STUDY FOR DISSIPATIVE NONLINEAR DRIFT IN INFINITE DIMENSION

AU - Albeverio, S

AU - Di Persio, L

AU - Mastrogiacomo, E

AU - Smii, Boubaker Abdelhafid Omar

PY - 2017

Y1 - 2017

N2 - We study a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Levy noise. We define a Hilbert-Banach setting in which we prove existence and uniqueness of solutions under general assumptions on the drift and the Levy noise. We then prove a decomposition of the solution process into a stationary component, the law of which is identified with the unique invariant probability measure mu of the process, and a component which vanishes asymptotically for large times in the L-P (mu)-sense, for all 1 <= p < + infinity.

AB - We study a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Levy noise. We define a Hilbert-Banach setting in which we prove existence and uniqueness of solutions under general assumptions on the drift and the Levy noise. We then prove a decomposition of the solution process into a stationary component, the law of which is identified with the unique invariant probability measure mu of the process, and a component which vanishes asymptotically for large times in the L-P (mu)-sense, for all 1 <= p < + infinity.

M3 - Article

SN - 1539-6746

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

ER -

INVARIANT MEASURES FOR SDES DRIVEN BY LEVY NOISE: A CASE STUDY FOR DISSIPATIVE NONLINEAR DRIFT IN INFINITE DIMENSION

Abstract

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