Stochastic calculus for fractional Brownian motion. I. Theory

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.