Ergodic Properties of Fractional Stochastic Burgers Equation

Zdzislaw Brzezniak; Latifa Debbi; Benjamin Goldys

Ergodic Properties of Fractional Stochastic Burgers Equation

Zdzislaw Brzezniak, Latifa Debbi, Benjamin Goldys

Mathematics

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

Abstract

We prove the existence and uniqueness of invariante measures for the fractional stochastic Burgers equation (FSBE) driven by the fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the solution converge to the invariante measure in the norm of total variation. To this end we show first two results which are of independent interest: that the semigroup corresponding to the solution of the FSBE is strong Feller and irreducible.

Original language	English
Pages (from-to)	145-174
Number of pages	30
Journal	Global and Stochastic Analysis
Volume	1
Issue number	2
Publication status	Published - Dec 2011

Keywords

Fractional stochastic partial differential equations, ergodic properties, invariant measure, strong Feller property, cylindrical Wiener noise.

Access to Document

Cite this

@article{f4e72390a91e4280aed1f4bcc90d6ae8,

title = "Ergodic Properties of Fractional Stochastic Burgers Equation",

abstract = "We prove the existence and uniqueness of invariante measures for the fractional stochastic Burgers equation (FSBE) driven by the fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the solution converge to the invariante measure in the norm of total variation. To this end we show first two results which are of independent interest: that the semigroup corresponding to the solution of the FSBE is strong Feller and irreducible.",

keywords = "Fractional stochastic partial differential equations, ergodic properties, invariant measure, strong Feller property, cylindrical Wiener noise.",

author = "Zdzislaw Brzezniak and Latifa Debbi and Benjamin Goldys",

year = "2011",

month = dec,

language = "English",

volume = "1",

pages = "145--174",

journal = "Global and Stochastic Analysis",

issn = "2248-9444",

publisher = "MUK Publications and Distribution",

number = "2",

}

TY - JOUR

T1 - Ergodic Properties of Fractional Stochastic Burgers Equation

AU - Brzezniak, Zdzislaw

AU - Debbi, Latifa

AU - Goldys, Benjamin

PY - 2011/12

Y1 - 2011/12

N2 - We prove the existence and uniqueness of invariante measures for the fractional stochastic Burgers equation (FSBE) driven by the fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the solution converge to the invariante measure in the norm of total variation. To this end we show first two results which are of independent interest: that the semigroup corresponding to the solution of the FSBE is strong Feller and irreducible.

AB - We prove the existence and uniqueness of invariante measures for the fractional stochastic Burgers equation (FSBE) driven by the fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the solution converge to the invariante measure in the norm of total variation. To this end we show first two results which are of independent interest: that the semigroup corresponding to the solution of the FSBE is strong Feller and irreducible.

KW - Fractional stochastic partial differential equations, ergodic properties, invariant measure, strong Feller property, cylindrical Wiener noise.

M3 - Article

SN - 2248-9444

VL - 1

SP - 145

EP - 174

JO - Global and Stochastic Analysis

JF - Global and Stochastic Analysis

IS - 2

ER -