Regularization of differential equations by fractional noise. (English) Zbl 1075.60536

Existence and uniqueness of a strong solution to the differential equation \[ X_t= x + \int _0^t b(s,X_s)\,ds + B^H_t, \quad t\geq 0, \] is established, where \(B^H_t\) is a fractional Brownian motion with the Hurst parameter \(H\in (0,1)\) and \(b(s,x)\) is a bounded Borel function with at most linear growth in \(x\) (for \(H\leq 1/2\)) or Hölder continuous function of order strictly larger than \(1-1/2H\) in \(x\) and \(H-1/2\) in time.


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G18 Self-similar stochastic processes
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