LINEAR MULTIFRACTIONAL STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

In this paper we prove the variation of parameters formula for linear Volterra integro-differential equations driven by multifractional Brownian motion. To do this, an approximation result for the Stratonovich stochastic integral with respect to the multifractional Brownian motion is given. Based on...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 1; pp. 333 - 350
Main Author Dung, Nguyen Tien
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.02.2013
Subjects
Brownian motion
Calculus
Mathematical independent variables
Mathematical integrals
Stochastic processes
Uniqueness
Volterra equations
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ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/tjm.17.2013.1728

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Summary:In this paper we prove the variation of parameters formula for linear Volterra integro-differential equations driven by multifractional Brownian motion. To do this, an approximation result for the Stratonovich stochastic integral with respect to the multifractional Brownian motion is given. Based on our obtained results we study the almost sure exponential convergence of the solution. Also, the existence and uniqueness of the solution of a multifractional Volterra integro-differential equation with time delay are proved. 2010Mathematics Subject Classification: 45D05, 60G22, 60H07. Key words and phrases: Volterra integro-differential equations, Variation of parameters formula, Multifractional Brownian motion, Malliavin calculus.
ISSN:1027-5487
2224-6851
2224-6851
DOI:10.11650/tjm.17.2013.1728