M ar 2 00 5 EXAMPLES OF MODERATE DEVIATION PRINCIPLE FOR DIFFUSION PROCESSES

Taking into account some likeness of moderate deviations (MD) and central limit theorems (CLT), we develop an approach, which made a good showing in CLT, for MD analysis of a family S κ t = 1 t κ t 0 H(Xs)ds, t → ∞ for an ergodic diffusion process Xt under 0.5 < κ < 1 and appropriate H. We mean a decomposition with " corrector " : 1 t κ t 0 H(Xs)ds = corrector + 1 t κ Mt martingale. and show that, as in the CLT analysis, the corrector is negligible but in the MD scale, and the main contribution in the MD brings the family " 1 t κ Mt, t → ∞. " Starting from Bayer and Freidlin, [2], and finishing by Wu's papers [29]-[33], in the MD study Laplace's transform dominates. In the paper, we replace the Laplace technique by one, admitting to give the conditions, providing the MD, in terms of " drift-diffusion " parameters and H. However, a verification of these conditions heavily depends on a specificity of a diffusion model. That is why the paper is named " Examples ... " .