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Stochastic calculus for fractional Brownian motion. I. Theory

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3 Author(s)
Duncan, T.E. ; Dept. of Math., Kansas Univ., Lawrence, KS, USA ; Hu, Y.Z. ; Pasik-Duncan, B.

Describes some of the results in Duncan et al. (2000) for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals are defined with explicit expressions for their first two moments. Multiple and iterated integrals of a fractional Brownian motion are defined and various properties of these integrals are given. A square integrable functional on a probability space of a fractional Brownian motion is expressed as an infinite series of multiple integrals

Published in:

Decision and Control, 2000. Proceedings of the 39th IEEE Conference on  (Volume:1 )

Date of Conference:

2000