Large deviations for a stochastic Volterra-type equation in the Besov-Orlicz space

Boualem Djehiche; M'Hamed Eddahbi

doi:10.1016/S0304-4149(98)00096-9

Large deviations for a stochastic Volterra-type equation in the Besov-Orlicz space

Boualem Djehiche, M'Hamed Eddahbi

Mathematics

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

Abstract

In this paper, we investigate the regularity of the solutions of a class of two-parameter Stochastic Volterra-type equations in the anisotropic Besov-Orlicz space B_τ,ω⁰ modulated by the Young function τ(t)=exp(t²)-1 and the modulus of continuity ω(t)=(t(1+log(1/t)))^1/2. Moreover, we derive in the Besov-Orlicz norm a large deviation estimate of Freidlin-Wentzell type for the solution.

Original language	English (US)
Pages (from-to)	39-72
Number of pages	34
Journal	Stochastic Processes and their Applications
Volume	81
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(98)00096-9
State	Published - May 1 1999

Keywords

60F17
Besov-Orlicz norm
Brownian sheet
Hyperbolic stochastic partial differential equation
Large deviations
Primary 92D30
Secondary 60J27
Volterra equation

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Access to Document

10.1016/S0304-4149(98)00096-9

Cite this

@article{c4464ed2c59947198f0a4ec89ee37921,

title = "Large deviations for a stochastic Volterra-type equation in the Besov-Orlicz space",

abstract = "In this paper, we investigate the regularity of the solutions of a class of two-parameter Stochastic Volterra-type equations in the anisotropic Besov-Orlicz space Bτ,ω0 modulated by the Young function τ(t)=exp(t2)-1 and the modulus of continuity ω(t)=(t(1+log(1/t)))1/2. Moreover, we derive in the Besov-Orlicz norm a large deviation estimate of Freidlin-Wentzell type for the solution.",

keywords = "60F17, Besov-Orlicz norm, Brownian sheet, Hyperbolic stochastic partial differential equation, Large deviations, Primary 92D30, Secondary 60J27, Volterra equation",

author = "Boualem Djehiche and M'Hamed Eddahbi",

year = "1999",

month = may,

day = "1",

doi = "10.1016/S0304-4149(98)00096-9",

language = "English (US)",

volume = "81",

pages = "39--72",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - Large deviations for a stochastic Volterra-type equation in the Besov-Orlicz space

AU - Djehiche, Boualem

AU - Eddahbi, M'Hamed

PY - 1999/5/1

Y1 - 1999/5/1

N2 - In this paper, we investigate the regularity of the solutions of a class of two-parameter Stochastic Volterra-type equations in the anisotropic Besov-Orlicz space Bτ,ω0 modulated by the Young function τ(t)=exp(t2)-1 and the modulus of continuity ω(t)=(t(1+log(1/t)))1/2. Moreover, we derive in the Besov-Orlicz norm a large deviation estimate of Freidlin-Wentzell type for the solution.

AB - In this paper, we investigate the regularity of the solutions of a class of two-parameter Stochastic Volterra-type equations in the anisotropic Besov-Orlicz space Bτ,ω0 modulated by the Young function τ(t)=exp(t2)-1 and the modulus of continuity ω(t)=(t(1+log(1/t)))1/2. Moreover, we derive in the Besov-Orlicz norm a large deviation estimate of Freidlin-Wentzell type for the solution.

KW - 60F17

KW - Besov-Orlicz norm

KW - Brownian sheet

KW - Hyperbolic stochastic partial differential equation

KW - Large deviations

KW - Primary 92D30

KW - Secondary 60J27

KW - Volterra equation

UR - http://www.scopus.com/inward/record.url?scp=0042597449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042597449&partnerID=8YFLogxK

U2 - 10.1016/S0304-4149(98)00096-9

DO - 10.1016/S0304-4149(98)00096-9

M3 - Article

AN - SCOPUS:0042597449

SN - 0304-4149

VL - 81

SP - 39

EP - 72

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Large deviations for a stochastic Volterra-type equation in the Besov-Orlicz space

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this