【摘 要】
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In this paper,we study a class of stochastic differential equations with additive noise that contains a non-stationary multifractional Brownian motion (mBm) wit
【机 构】
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School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
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In this paper,we study a class of stochastic differential equations with additive noise that contains a non-stationary multifractional Brownian motion (mBm) with a Hurst parameter as a function of time and a Poisson point process of class (QL).The differential equation of this kind is motivated by the reserve processes in a general insurance model,in which between the claim payment and the past history of liability present the long term dependence.By using the variable order fractional calculus on the fractional Wiener-Poisson space and a multifractional derivative operator,and employing Girsanov theorem for multifractional Brownian motion,we prove the existence of weak solutions to the SDEs under consideration,As a consequence,we deduce the uniqueness in law and the pathwise uniqueness.
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