Revistes Catalanes amb Accés Obert (RACO)

Differential equations driven by fractional Brownian motion

David Nualart, Aurel Rascanu


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 $H > {1\over 2}$ 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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