The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6
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چکیده
Let B be a fractional Brownian motion with Hurst parameter H = 1/6. It is known that the symmetric Stratonovich-style Riemann sums for ∫ g(B(s)) dB(s) do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of càdlàg functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Itô integral with respect to a Brownian motion that is independent of B. AMS subject classifications: Primary 60H05; secondary 60G15, 60G18, 60J05.
منابع مشابه
m-order integrals and generalized Ito’s formula; the case of a fractional Brownian motion with any Hurst index
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 fo...
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تاریخ انتشار 2010