Some It formulas with respect to mixed Fractional Brownian motion and Brownian motion were given in this paper.These extended the It formula for the fractional Wick It Skorohod integral with respect to Fractional Brownian motion,meanwhile extended the It formula for It Skorohod integral with respect to Brownian motion.Taylor's formula is applied to prove our conclusion in this article.
This paper is concerned with the stochastically stability for the m-dimensional linear stochastic differential equations with respect to fractional Brownian motion(FBM)with Hurst parameter H∈(1/2,1).On the basis of the pioneering work of Duncan and Hu,a It's formula is given.An improved derivative operator to Lyapunov functions is constructed,and the sufficient conditions for the stochastically stability of linear stochastic differential equations driven by FBM are established.These extend the stochastic Lyapunov stability theories.
