Diffusion approximation for slow motion in fully coupled averaging. (English) Zbl 1069.34070

Bakhtin, Victor; Kifer, Yuri

Probab. Theory Relat. Fields 129, No. 2, 157-181 (2004).

Fast and slow motions are averaged as fully coupled diffusion processes. The authors prove the existence of another diffusion process which \(L^2\)-approximates the slow motion much better than the averaged motion prescribed by the averaging principle.

Reviewer: George Stoica (Saint John)

MSC:

34C29	Averaging method for ordinary differential equations
60F15	Strong limit theorems
58J65	Diffusion processes and stochastic analysis on manifolds
34E13	Multiple scale methods for ordinary differential equations

Keywords:

slow-fast motion; averaging principle