Ito Formula and Local Time for the Fractional Brownian Sheet

Ciprian A. Tudor (Laboratoire de Probabilit'{e}s, Universit'{e} de Paris 6)
Frederi G. Viens (Purdue University)

Abstract


Using the techniques of the stochastic calculus of variations for Gaussian processes, we derive an It^{o} formula for the fractional Brownian sheet with Hurst parameters bigger than $1/2$. As an application, we give a stochastic integral representation for the local time of the fractional Brownian sheet.

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Pages: 1-31

Publication Date: August 21, 2003

DOI: 10.1214/EJP.v8-155

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