Advances in Difference Equations · 2015 · 34 citations · 16 references
EngineeringMathematicsDifferential EquationsProbability TheoryStochastic ProcessesContinuous-time Stochastic ProcessesDiffusion ProcessesJump ProcessesStochastic CalculusStochastic ControlStochastic Differential EquationsBurkholder-davis-gundy InequalitiesDelay EquationsItô CalculusItô's LemmaJump-diffusion ProcessesStochastic Delay SystemsStochastic Integration
In this paper, we investigate the averaging principle for stochastic delay differential equations (SDDEs) and SDDEs with pure jumps. By the Itô formula, the Taylor formula, and the Burkholder-Davis-Gundy inequality, we show that the solution of the averaged SDDEs converges to that of the standard SDDEs in the sense of pth moment and also in probability. Finally, two examples are provided to illustrate the theory.
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