TAIWANESE JOURNAL OF MATHEMATICS

Vol. 5, No. 3, pp. 609-632,  September 2001

　

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    STOCHASTIC STRATONOVICH CALCULUS fBm FOR FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER LESS THAN 1/2

　

E. Alòs, J. A. León* and D. Nualart+
　

Abstract.
              In this paper we introduce a Stratonovich type stochastic integral with respect to the fractional Brownian motion with Hurst parameter less than 1/2. Using the techniques of the Malliavin calculus, we provide sufficient conditions for a process to be integrable. We deduce an Itô formula and we apply these results to study stochastic differential equations driven by a fractional Brownian motion with Hurst parameter less than 1/2.

　

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Received June 1, 2000; revised June 30, 2000.

Communicated by Y.-J. Lee.

2000 Mathematics Subject Classification: 60H05, 60H07.

Key words and phrases: Stochastic calculus, Stratonovich integral, Malliavin calculus, factional Brownian motion, stochastic differential equations.

*Supported by the CONACyT grant no. 27932-E.

+Supported by the DGYCIT grant no. PB96-0087.