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Linear multifractional stochastic Volterra integro-differential equations. (English) Zbl 1339.45006
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 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.

MSC:
45J05 Integro-ordinary differential equations
45D05 Volterra integral equations
45R05 Random integral equations
60J65 Brownian motion
60H20 Stochastic integral equations
45A05 Linear integral equations
60H07 Stochastic calculus of variations and the Malliavin calculus
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