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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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
Online AccessGet full text
ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/tjm.17.2013.1728

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Abstract 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.
AbstractList 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.
Author Dung, Nguyen Tien
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Cites_doi 10.1080/17442509808834172
10.1007/s11009-010-9188-5
10.3150/10-BEJ261
10.57262/die/1372700426
10.1088/0305-4470/34/7/306
10.1214/EJP.v8-179
10.1214/aop/1008956692
10.1090/S0002-9939-1969-0247016-9
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SubjectTerms Brownian motion
Calculus
Mathematical independent variables
Mathematical integrals
Stochastic processes
Uniqueness
Volterra equations
Title LINEAR MULTIFRACTIONAL STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
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