Karhunen - Loève expansions of mean - centered Wiener processes
نویسنده
چکیده
For γ > − 1 2 , we provide the Karhunen-Lò eve expansion of the weighted mean-centered Wiener process , defined by Wγ (t) = 1 √ 1 + 2γ W t 1+2γ − 1 0 W u 1+2γ du , for t ∈ (0 , 1 ]. We show that the orthogonal functions in these expansions have simple expressions in term of Bessel functions. Moreover , we obtain that the L 2 [ 0 , 1 ] norm of Wγ is identical in distribution with the L 2 [ 0 , 1 ] norm of the weighted Brownian bridge t γ B (t) .
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تاریخ انتشار 2006