m-order integrals and generalized Ito’s formula; the case of a fractional Brownian motion with any Hurst index
نویسندگان
چکیده
Given an integer m, a probability measure ν on [0, 1], a process X and a real function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the fractional Brownian motion B , for any locally bounded function g, the corresponding integral vanishes for all odd indices m > 1 2H and any symmetric ν. One consequence is an Itô-Stratonovich type expansion for the fractional Brownian motion with arbitrary Hurst index H ∈]0, 1[. On the other hand we show that the classical Itô-Stratonovich formula holds if and only if H > 1 6 .
منابع مشابه
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