F. Klebaner, R. Liptser
The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.
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Sample-path large deviations for a class of heavy-tailed Markov additive processes
本文针对由仿射递归驱动的重尾马尔可夫可加过程，在$M_1'$拓扑下发展了样本路径大偏差原理，并揭示了最可能路径为含正负跳的阶跃函数。
We consider the linear stochastic recursion $x_{i+1} = a_{i}x_{i}+b_{i}$ where the multipliers $a_i$ are random and have Markovian dependence given by the exponential of a standard Brownian motion and $b_{i}$ are i.i.d. positive random noise independent of $a_{i}$. Using large deviations theory we study the growth rates (Lyapunov exponents) of the positive integer moments $λ_q = \lim_{n\to \infty} \frac{1}{n} \log\mathbb{E}[(x_n)^q]$ with $q\in \mathbb{Z}_+$. We show that the Lyapunov exponents $λ_q$ exist, under appropriate scaling of the model parameters, and have non-analytic behavior manif…
Sample-path large deviations for unbounded additive functionals of the reflected random walk
本文研究 Lindley 递归 Markov 链无界泛函的样本路径大偏差，利用再生周期分解在 M_1' 拓扑下证明次线性速度 LDP，并揭示 MRW 繁忙期面积的重尾特性。
We study the situations when the solution to a weighted stochastic recursion has a power law tail. To this end, we develop two complementary approaches, the first one extends Goldie's (1991) implicit renewal theorem to cover recursions on trees; and the second one is based on a direct sample path large deviations analysis of weighted recursive random sums. We believe that these methods may be of independent interest in the analysis of more general weighted branching processes as well as in the analysis of algorithms.
Large Deviations for Controlled Branching Processes: Random Slopes, Harmonic Moments, and Transfer Principles
该论文研究受控分支过程在超临界和临界状态下三个比率的大偏差，通过随机斜率与转移原理建立精确上尾渐近，并揭示一阶随机性位置决定下尾机制、移民影响衰减指数等结论。
Large deviation principles and functional limit theorems in the deep limit of wide random neural networks
本文研究了广泛随机神经网络中大偏差原理和函数极限定理，通过分析协方差函数的递归演变，揭示了不同 disorder regime 下的统计动态特性。
Moderate Deviation Principle for a Stochastic Approximation Process
本文研究了一个取值于实数空间的随机逼近过程，通过递推关系建立其中偏差原理，并推导了指数不等式和加权和的中偏差原理。
A quenched large deviation principle for Brownian motion in a non-negative, stationary potential is proved. A sufficient moment condition on the potential is given but unlike the results of Armstrong and Tran (2014) no regularity is assumed. The proof is based on a method developed by Sznitman (1994) for Brownian motion among Poissonian potential. In particular, the LDP holds for potentials with polynomially decaying correlations such as the classical potentials studied by L. Pastur (1977) and R. Fukushima (2008) and the potentials recently introduced by H. Lacoin (2012).
Sample Path Moderate Deviation Principle for Queues with Waiting-time Dependent Interarrival and Service Times
该研究针对等待时间依赖到达间隔与服务时间的单服务台队列，建立样本路径中偏差原理，明确了两种情形下的速率函数，采用鞅技术完成分析。
Large deviations principle for a stochastic process with random reinforced relocations
本文研究具有随机强化重定位的非马尔可夫随机过程，在随机重定位间隔构成随机环境的条件下，证明了其长时间取值的淬灭大偏差原理。
Moderate Deviations for Nonlinear Hawkes Processes
本文为非线性霍克斯过程建立完全适度区间内的样本路径适度偏差原理，通过构造泊松校正子并利用鞅方法，得到介于中心极限与大偏差尺度间的结果，并给出渐近方差响应公式。
Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. Steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes have not been rigorously proved yet due to technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loéve expansion of complex-valued Ornstein-Uhlenbeck pro…
Spectral theory for dynamical large deviations in non-Markov self-interacting processes
本文为非马尔可夫自相互作用过程建立动力学大偏差的谱理论，通过多尺度WKBJ拟设简化Feynman-Kac方程为特征值问题，并用双稳态East模型验证，提供高效计算框架。
Large Deviation Principle for Last Passage Percolation Models
本文应用并改进已有框架，在不依赖精确可解性的条件下为末次穿越渗流（LPP）模型建立了度量层面的大偏差原理，并据此推导出测地线的大偏差原理，为研究测地线大横向涨落提供了简化方法。
Level 2.5 large deviations and uncertainty relations for non-Markov self-interacting dynamics
本文研究非马尔可夫系统的大偏差问题，提出二级大偏差联合统计方法，推导轨迹可观测量波动的一般界限，并通过实例展示其应用。
Quenched large deviation principles for random projections of $\ell_p^n$ balls
本文研究了适当缩放的 $\ell_p^n$-球或球面及次高斯乘积分布的 $k_n$ 维随机正交投影序列在投影维数次线性增长时的淬火大偏差原理，获得了不依赖投影矩阵的显式速率函数及相关范数推论，并建立了Stiefel流形上的新高斯逼近结果。
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