Existence of Solutions for Stochastic Differential Equations under G-Brownian Motion with Discontinuous Coefficients
نویسنده
چکیده
The existence theory for the vector valued stochastic differential equations under G-Brownian motion (G-SDEs) of the type Xt = X0 + ∫ t 0 f (v,Xv)dv+ ∫ t 0 g(v,Xv)d〈B〉v + ∫ t 0 h(v,Xv)dBv, t ∈ [0,T ], with first two discontinuous coefficients is established. It is shown that the G-SDEs have more than one solution if the coefficient g or the coefficients f and g simultaneously, are discontinuous functions. The upper and lower solutions method is used and examples are given to explain the theory and its importance.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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