Large deviations for infinite dimensional stochastic dynamical systems
Large deviations for infinite dimensional stochastic dynamical systems
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DOI：
10.1214/07-aop362
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发表时间：
2008-08
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影响因子：
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通讯作者：
A. Budhiraja;P. Dupuis;V. Maroulas
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文献类型：
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作者：
A. Budhiraja;P. Dupuis;V. Maroulas
随机微分方程及相关过程解的大偏差分析往往是基于近似的。近似的构造和证明可能是繁重的，特别是在过程状态是无限维的情况下。在本文中，我们将展示如何避免这种近似的各种无限维模型驱动的某种形式的布朗噪声。该方法是基于布朗运动泛函的变分表示。大偏差性质的证明减少到证明原始过程的某些扰动的基本定性性质（存在性、唯一性和紧密性）。
The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of Brownian motion. Proofs of large deviations properties are reduced to demonstrating basic qualitative properties (existence, uniqueness and tightness) of certain perturbations of the original process.