APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC SYSTEMS DRIVEN BY ROSENBLATT PROCESS AND BROWNIAN MOTION

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion

Constrained controllability of nonlinear stochastic impulsive systems

There are many real-world systems and natural processes which display some kind of dynamic behavior in a style of both continuous and discrete characteristics. For instance, many evolutionary processes, particularly some biological systems such as biological neural networks and bursting rhythm models in pathology, as well as optimal control models in economics, frequency-modulated signal proces...

Stochastic Impulsive Systems Driven by Renewal Processes

Abstract— Stochastic impulsive systems are defined by a diffusion process with jumps triggered by a renewal process, i.e., the intervals between jumps are independent and identically distributed. We construct a model for such systems based on jump-diffusion equations and provide Lyapunov-based conditions that guarantee their mean-square stability. As an application, we show that stochastic impu...

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...