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Existence and uniqueness theorems for fBm stochastic differential equations. (English. Russian original) Zbl 0924.60042
Probl. Inf. Transm. 34, No. 4, 332-341 (1998); translation from Probl. Peredachi. Inf. 34, No. 4, 51-61 (1998).
Conditions are identified and then proofs are given that establish existence and uniqueness of the solution of stochastic ordinary differential equations of the following two forms: \[ dX_t= a(t,X_t)dt+ b(t,X_t)dB_t^h, \qquad X_0=x, \tag{1} \] where \(B_t^h\) is a scalar fractional Brownian motion with Hurst index \(h\) between \(\frac 12\) and 1, \[ dX_t= a(t,X_t)dt+ dB_t^h, \qquad X_0=x, \tag{2} \] where \(B_t^h\) is a \(d\)-dimensional vector fractional Brownian motion with Hurst index \(h\) between \(\frac 12\) and 1.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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