随机环境下一维扩散的小时间退火大偏差原理
Small-time annealed large deviations principle for one-dimensional diffusions in a random environment
- University of Science and Technology of China（中国科学技术大学）
- University of Manchester（曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对随机环境下一维扩散，借助扩散的伊藤-麦肯表示与Moser迭代得到的首出时概率估计，建立了小时间退火路径大偏差原理，涵盖了被广泛研究的Brox扩散模型。
AI中文摘要：
本文针对与生成元${\mathcal L}_W f(x)=e^{-ρ(x,W)}(e^{a(x,W)}f'(x))'$相关的随机环境下一维扩散，建立了小时间退火路径大偏差原理。系数$\{ρ(x,\cdot):x\in\mathbb R\}$和$\{a(x,\cdot):x\in\mathbb R\\
英文摘要：
In this paper, we establish a small-time annealed path large deviation principle for one-dimensional diffusions in a random environment associated with the generator ${\mathcal L}_W f(x)=e^{-ρ(x,W)}(e^{a(x,W)}f'(x))'$. The coefficients $\{ρ(x,\cdot):x\in\mathbb R\}$ and $\{a(x,\cdot):x\in\mathbb R\}$ are random. We assume that for each fixed realization of the environment, $ρ$ and $a$ are continuous and locally exponentially integrable, and that the support of the associated intrinsic coordinates is compact and non-collapsing. This framework includes the extensively studied Brox diffusion $dX_t=dB_t-\frac12\dot W(X_t)\,dt$, where $B$ is a standard Brownian motion and $W$ is an independent two-sided Brownian motion representing the environment. The Itô--McKean representation of the diffusions and the estimates of the first exit probabilities derived via Moser iteration play a crucial role.
