Existence and uniqueness results for impulsive hybrid stochastic delay systems. (English) Zbl 1225.34089

Liu, Jun; Liu, Xinzhi; Xie, Wei-Chau

Commun. Appl. Nonlinear Anal. 17, No. 3, 37-53 (2010).

Summary: This paper investigates the existence and uniqueness of solutions for a general class of impulsive and switched hybrid stochastic delay systems. Due to the impulse effects and time delay, solutions of an impulsive and switched hybrid stochastic delay system have to be formulated and considered to be evolving in the space of piecewise continuous functions on the delay interval. The basic theory established here can also be applied to impulsive stochastic functional differential equations as a special case.

MSC:

34K50	Stochastic functional-differential equations
34K45	Functional-differential equations with impulses
93C30	Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
34K34	Hybrid systems of functional-differential equations
34A36	Discontinuous ordinary differential equations

Keywords:

existence; uniqueness; impulsive differential equation; stochastic differential equation; functional differential equation; hybrid system; time-delay