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Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion

Tianyang Nie;  Aurel Răşcanu — 2012

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, using direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution of a given stochastic differential equation driven by the fractional Brownian motion evolves in some particular sets . As a consequence, a comparison theorem is obtained.

Differential equations driven by fractional Brownian motion.

David Nualart;  Aurel Rascanu — 2002

Collectanea Mathematica

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

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