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A new proof of fractional Hu-Meyer formula and its applications. (English) Zbl 1283.60072

Summary: 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:

60G22 Fractional processes, including fractional Brownian motion
60H05 Stochastic integrals
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[1] doi:10.1137/S036301299834171X · Zbl 0947.60061 · doi:10.1137/S036301299834171X
[2] doi:10.1016/j.spa.2005.09.009 · Zbl 1088.60053 · doi:10.1016/j.spa.2005.09.009
[3] doi:10.1016/S0304-4149(03)00018-8 · Zbl 1075.60533 · doi:10.1016/S0304-4149(03)00018-8
[4] doi:10.1007/s10959-006-0006-5 · Zbl 1103.60055 · doi:10.1007/s10959-006-0006-5
[5] doi:10.1214/aop/1176995480 · Zbl 0387.60064 · doi:10.1214/aop/1176995480
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