Taiwanese Journal of Mathematics

LINEAR MULTIFRACTIONAL STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Tien Dung Nguyen

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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 approximate result for the Stratonovich stochastic integral with respect to the multifractional Brownian motion is given. Based on our obtained results we study almost surely exponentially convergence of the solution. Also, the existence and uniqueness of the solution of a multifractional Volterra integro-differential equation with time delay are proved.

Article information

Source
Taiwanese J. Math., Volume 17, Number 1 (2013), 333-350.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705891

Digital Object Identifier
doi:10.11650/tjm.17.2013.1728

Mathematical Reviews number (MathSciNet)
MR3028873

Zentralblatt MATH identifier
1339.45006

Subjects
Primary: 45D05: Volterra integral equations [See also 34A12] 60G22: Fractional processes, including fractional Brownian motion 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
Volterra integro-differential equations variation of parameters formula multifractional Brownian motion Malliavin calculus

Citation

Nguyen, Tien Dung. LINEAR MULTIFRACTIONAL STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS. Taiwanese J. Math. 17 (2013), no. 1, 333--350. doi:10.11650/tjm.17.2013.1728. https://projecteuclid.org/euclid.twjm/1499705891


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