MDP for integral functionals of fast and slow processes with averaging

Details MDP for integral functionals of fast and slow processes with averaging MDP for integral functionals of fast and slow processes with averaging

2003-04-27

arxiv.org/abs/math/0304426v1

Mathematics

Probability

18 pages

Scientific paper

We establish large deviation principle (LDP) for the family of vector-valued random processes $(X^\epsilon,Y^\epsilon),\epsilon\to 0$ defined as $$ X^\epsilon_t=\frac{1}{\epsilon^\kappa}\int_0^t H(\xi^\epsilon_s,Y^\epsilon_s)ds, dY^\epsilon_t=F(\xi^\epsilon_t,Y^\epsilon_t)dt+ D\epsilon^{1/2-\kappa}G(\xi^\epsilon_t,Y^\epsilon_t)dW_t,$$ where $W_t$ is Wiener process and $\xi^\epsilon_t$ is fast ergodic diffusion. We show that, under $\kappa<{1/2}$ or less and Veretennikov-Khasminskii type condition for fast diffusion, the LDP holds with rate function of Freidlin-Wentzell's type.

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