LINEAR MULTIFRACTIONAL STOCHASTIC VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS - Dung, Nguyen Tien (Taiwanese journal of mathematics, 2013)
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.