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

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.

MSC:

 60H05 Stochastic integrals 60H07 Stochastic calculus of variations and the Malliavin calculus
Full Text: