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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)