Random perturbations of dynamical systems and diffusion processes with conservation laws. (English) Zbl 1044.60044
The authors are concerned with random perturbations of dynamical systems and diffusion processes with a first integral. For a general class of perturbations, and under an appropriate time scale, the behaviour of the slow component of the perturbed system is calculated. Consideration of diffusion processes in this light leads to a study of the multidimensional case, and it is shown that the limiting slow motion can spend non-zero time at some points of a specific graph. More general glueing conditions are obtained, and specific attention is paid to singular perturbations of PDE’s.
Reviewer: Andrew Dale (Durban)
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34C29 | Averaging method for ordinary differential equations |
| 35B20 | Perturbations in context of PDEs |
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