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The Bouleau–Yor identity for a bi-fractional Brownian motion

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Let B be a bi-fractional Brownian motion with indices [Inline formula], [Inline formula] and let [Inline formula] be its local time process. We construct a Banach space [Inline formula] of measurable functions such that the quadratic covariation [Inline formula] and the integral [Inline formula] exist provided [Inline formula]. Moreover, the Bouleau–Yor identityholds for all [Inline formula].
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Keywords: 60G15; 60G17; 60H05; Itô formula; bi-fractional Brownian motion; local time; quadratic covariation; stochastic integration

Document Type: Research Article

Affiliations: 1: Department of Mathematics, Donghua University, 2999 North Renmin Road, Songjiang, Shanghai,201620, P.R. China 2: School of Mathematics and Statistics, Nanjing Audit University, 86 West Yushan Road, Pukou, Nanjing,211815, P.R. China

Publication date: May 4, 2014

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