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Chaos expansion of local time of fractional Brownian motions
Hu, Yaozhong Oksendal, Bernt
Hu, Yaozhong
Oksendal, Bernt
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Abstract
We find the chaos expansion of local time l(T)((H))(x, (.)) of fractional Brownian motion with Hurst coefficient H is an element of (0, 1) at a point x is an element of R-d. As an application we show that when H(0)d < 1 then l(T)((H))(x, (.)) is an element of L-2(mu). Here mu denotes the probability law of B-(H) and H-0 = max {H-1, ..., H-d}. In particular, we show that when d = 1 then l(T)((H))(x, (.)) is an element of L-2(mu) for all H is an element of (0, 1).
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Date
2002-07
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MARCEL DEKKER INC
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Keywords
Fractional brownian motion, Chaos expansion, Local time, Asymptotic behavior
Citation
Hu, YZ; Oksendal, B. Chaos expansion of local time of fractional Brownian motions. STOCHASTIC ANALYSIS AND APPLICATIONS. July 2002. 20(4):815-837