Examples of moderate deviation principle for diffusion processes

By Arnaud Guillin, Robert Sh. Liptser. 2005

49 citations recorded by the source corpus.

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 $S^\kappa_t=\frac{1}{t^\kappa}\int_0^tH(X_s)ds, t\to\infty$ for an ergodic diffusion process $X_t$, provided that $0.5<\kappa<1$, and appropriate $H$. We use a well known decomposition with "corrector'': $\frac{1}{t^\kappa}\int_0^tH(X_s)ds=$corrector$+\frac{1}{t^\kappa}$ ${M_t}$martingale. and show that, as in the CLT analysis, the corrector is negligible, and the main contribution in the MD brings the family "$ \frac{1}{t^\kappa}M_t, \ t\to\infty. $'' Starting from Freidlin, [7], and finishing by Wu's papers [33]-[37], in the MD study Laplace's transform dominates. In the paper, we replace this technique by "Stochastic exponential'' one, enabling to formulate the MDP conditions 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 ...''.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7d7038ccc5e1592468618f6f063d43961ee1f5bf

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Citations in the corpus

A moderate deviation principle for 2-D stochastic Navier-Stokes equations (2015, methodology): “[12] A. Guillin and R. Liptser (2006).”
A Moderate Deviation Principle for 2-D Stochastic Navier-Stokes Equations Driven by Multiplicative L\'evy Noises (2015, methodology): “, Wu [24] for Markov processes, Guillin and Liptser [12] for diffusion processes, Wang and Zhang [23] for stochastic reaction-diffusion equations.”