Differential equations driven by fractional Brownian motion. (English) Zbl 1018.60057

Nualart, David; Răşcanu, Aurel

Collect. Math. 53, No. 1, 55-81 (2002).

The authors consider stochastic differential equations driven by a fractional Brownian motion with Hurst parameter \(H>1/2\), where stochastic integrals are defined pathwise in the Riemann-Stieltjes sense. They present a global existence and uniqueness result for the solutions of such stochastic differential equations in the multidimensional case, with time-dependent coefficients satisfying Lipschitz and Hölder assumptions. The proof relies on an existence and uniqueness theorem for deterministic differential equations, which is based on a contraction principle in Hölder and Besov norms.

Reviewer: Nicolas Privault (La Rochelle)

MSC:

60H05	Stochastic integrals
60H07	Stochastic calculus of variations and the Malliavin calculus

Keywords:

stochastic differential equations; fractional Brownian motion