论文标题
通向白噪声混乱扩展的大偏差
Pathwise large deviations for white noise chaos expansions
论文作者
论文摘要
We consider a family of continuous processes $\{X^\varepsilon\}_{\varepsilon>0}$ which are measurable with respect to a white noise measure, take values in the space of continuous functions $C([0,1]^d:\mathbb{R})$, and have the Wiener chaos expansion \ [ x^\ varepsilon = \ sum_ {n = 0}^{\ infty} \ varepsilon^n i_n i_n \ big（f_n^{\ varepsilon} \ big）。 \]我们为$ \ {x^\ varepsilon \} _ {\ varepsilon> 0} $的大偏差原理提供了足够的条件，以在$ c（[0,1]^d：\ mathbb {r}）$中保留，从而使Pérez-abree castion（19933 ins the the Iss to refress of to refress of to refress ins of the hisk of the hight of the of the of the highien of the highian in theirian castion in theirian castion（19933）。证明基于对大偏差的弱收敛方法：它涉及证明原始过程某些扰动分布的收敛性，因此主要的困难在于分析和控制扰动的多个随机积分。此外，采用此表示形式提供了有关路径大偏差的新观点，并引起了多种应用。
We consider a family of continuous processes $\{X^\varepsilon\}_{\varepsilon>0}$ which are measurable with respect to a white noise measure, take values in the space of continuous functions $C([0,1]^d:\mathbb{R})$, and have the Wiener chaos expansion \[ X^\varepsilon = \sum_{n=0}^{\infty} \varepsilon^n I_n \big(f_n^{\varepsilon} \big). \] We provide sufficient conditions for the large deviations principle of $\{X^\varepsilon\}_{\varepsilon>0}$ to hold in $C([0,1]^d:\mathbb{R})$, thereby refreshing a problem left open by Pérez-Abreu (1993) in the Brownian motion case. The proof is based on the weak convergence approach to large deviations: it involves demonstrating the convergence in distribution of certain perturbations of the original process, and thus the main difficulties lie in analysing and controlling the perturbed multiple stochastic integrals. Moreover, adopting this representation offers a new perspective on pathwise large deviations and induces a variety of applications thereof.
