Examples of moderate deviation principle for diffusion processes

摘要: 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 family $$ S^\kappa_t=\frac{1}{t^\kappa}\int_0^tH(X_s)ds, \ t\to\infty ergodic diffusion process $X_t$ under $0.5<\kappa<1$ appropriate $H$. We mean decomposition with ``corrector'': \frac{1}{t^\kappa}\int_0^tH(X_s)ds={\rm corrector}+\frac{1}{t^\kappa}\underbrace{M_t}_{\rm martingale}. show that, as the CLT analysis, corrector is negligible but scale, main contribution brings ``$ \frac{1}{t^\kappa}M_t, t\to\infty. $'' Starting from Bayer Freidlin, \cite{BF}, finishing by Wu's papers \cite{Wu1}-\cite{WuH}, study Laplace's transform dominates. In paper, replace Laplace technique one, admitting to give conditions, providing MD, terms ``drift-diffusion'' parameters However, verification these conditions heavily depends on specificity model. That why paper named ``Examples ...''.