Averaging principle and systems of singularly perturbed stochastic differential equations. (English) Zbl 0701.60057
Summary: By developing certain auxiliary results, a modified version of the stochastic averaging principle is developed to investigate dynamical systems consisting of fast and slow phenomena. Moreover, an attempt is made to establish a relationship between the averaging assumption and certain ergodic-type properties of the random process determined by an auxiliary system of stochastic differential equations. Finally, an example is given to illustrate the scope of the results.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
References:
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| [2] | G. S. Ladde and V. Lakshmikantham,Random Differential Inequalities(Academic, New York, 1980). · Zbl 0466.60002 |
| [3] | A. Friedman,Stochastic Differential Equations and Applications(Academic, New York, 1975), Vol. I. · Zbl 0323.60056 |
| [4] | D. D. Siljak,Large-Scale Dynamical Systems: Stability and Structure(North-Holland, New York, 1978). · Zbl 0384.93002 |
| [5] | N. Ikeda, and S. Watanabe,Stochastic Differential Equations and Diffusion Processes(North-Holland, Amsterdam, 1981). · Zbl 0495.60005 |
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