Title :
Stochastic calculus for fractional Brownian motion. I. Theory
Author :
Duncan, T.E. ; Hu, Y.Z. ; Pasik-Duncan, B.
Author_Institution :
Dept. of Math., Kansas Univ., Lawrence, KS, USA
Abstract :
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
Keywords :
Brownian motion; Hilbert spaces; integral equations; integration; probability; Hurst parameter; fractional Brownian motion; iterated integrals; multiple integrals; probability space; square integrable functional; stochastic calculus; stochastic integrals; Brownian motion; Calculus; Gaussian processes; Mathematics; Polynomials; Probability; Reservoirs; Rivers; Stochastic processes; Topology;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2000.912761
