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Zbl 1225.34089
Liu, Jun; Liu, Xinzhi; Xie, Wei-Chau
Existence and uniqueness results for impulsive hybrid stochastic delay systems. (English)
[J] Commun. Appl. Nonlinear Anal. 17, No. 3, 37-53 (2010). ISSN 1074-133X

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 2000:: *34K50 Stochastic delay equations
34K45 Equations with impulses
93C30 Control systems governed by other functional relations
34K34
34A36 Discontinuous equations

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

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Zentralblatt MATH Berlin [Germany]