p-variation of an integral functional associated with bi-fractional Brownian motion | Zendy

Junfeng Liu | Zendy; Litan Yan | Zendy; Tang Donglei | Zendy

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p-variation of an integral functional associated with bi-fractional Brownian motion

Author(s) -

Junfeng Liu,

Litan Yan,

Tang Donglei

Publication year - 2013

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1306995l

Subject(s) - mathematics , brownian motion , fractional brownian motion , constant (computer programming) , motion (physics) , variation (astronomy) , combinatorics , mathematical analysis , mathematical physics , physics , classical mechanics , statistics , computer science , astrophysics , programming language

In this paper we consider the functionals A1(t,x) = integral(t)(0) 1 (0,∞)(x-BsH,K)dS A2(t,x) = integral(t)(0) 1 (0,∞)(x-BsH,K)S2HK-1dS, where BH,K is a bifractional Brownian motion with indices H є (0,1), K є (0,1]. We find a constant pH,K є (1,2) such that p-variation of the process Aj(t, BsH,K) integral(t)(0) Z j(s, BsH,K)dBsH,K (j = 1,2) equals to 0 if p > pHK, where Zi, j = 1,2, are the local times of BtH,K. This extends the classical results for Brownian motion (Rogers-Walsh [17]). .

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