Existence and uniqueness theorems for fBm stochastic differential equations
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.
stochastic ordinary differential equations
scientific article; zbMATH DE number 1294990