Abstract
This paper is concerned with the Hu-Meyer formula for fractional Brownian motion with the Hurst parameter less than 1/2. By the mollifier approximation, the Hu-Meyer formula is explicitly obtained based on the multiple Stratonovich integral, and the proof is different from the known methods. Moreover, the obtained Hu-Meyer formula can be applied to derive the convergence rate of the multiple fractional Stratonovich integral. MSC: 60G15; 62H05
Highlights
1 Introduction It is well known that Hu and Meyer [ ] introduced a new multiple stochastic integral with respect to a Wiener process, called a multiple Stratonovich integral, which is in general different from the usually studied multiple Wiener-Itô integral
The authors proposed a formula that gives the relationship of the Stratonovich integral with the Itô integrals of some functions called the traces that involve integrals of f on the diagonals
Section recalls some results from [ ] on the multiple Stratonovich integral, which will be used in the remainder of the paper
Summary
It is well known that Hu and Meyer [ ] introduced a new multiple stochastic integral with respect to a Wiener process, called a multiple Stratonovich integral, which is in general different from the usually studied multiple Wiener-Itô integral. Many authors have considered an integral with respect to fBm. Duncan et al [ ] employed the Wick products to define a fractional stochastic integral whose mean is zero. They defined the traces to obtain the Hu-Meyer formula that gives the Stratonovich integral as a sum of Itô integrals of these traces. We consider a similar problem for the multiple Stratonovich integral.
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