具有独立增量的非负多元点过程的Cramer定理

具有非负相关增量的高斯过程高极小值的大偏差

Large Deviations for High Minima of Gaussian Processes with Nonnegatively Correlated Increments

针对具有非负相关增量的高斯过程，研究其高极小值及特定区间上增量的大偏差原理，并以H≥1/2的分数布朗运动和分数高斯噪声为例。

Cramer破产定理的对数形式对某些FARIMA及相关过程的推广

An extension of a logarithmic form of Cramer's ruin theorem to some FARIMA and related processes

Cramer定理提供了负漂移和增量的随机游动的最大值的尾概率的估计，该随机游动在原点的邻域中具有有限的矩母函数。这类（g，F）过程以自然的方式推广了时间序列分析中使用的随机游动和分数ARIMA模型。对于那些（g，F）-过程的负漂移，我们得到了对数估计的尾部概率的最大值，条件下相媲美Cramer的。此外，我们展示了最有可能的路径，以及最有可能的行为的创新导致一个大的最大值。

Contraction principle for trajectories of random walks and Cramer's theorem for kernel-weighted sums

In 2013 A.A. Borovkov and A.A. Mogulskii proved a weaker-than-standard "metric" large deviations principle (LDP) for trajectories of random walks in $R^d$ whose increments have the Laplace transform finite in a neighbourhood of zero. We prove that general metric LDPs are preserved under uniformly continuous mappings. This allows us to transform the result of Borovkov and Mogulskii into standard LDPs. We also give an explicit integral representation of the rate function they found. As an application, we extend the classical Cram'er theorem by proving an LPD for kernel-weighted sums of i.i.d. ra…

通过非负超鞅获得时间均匀Chernoff界

Time-uniform Chernoff bounds via nonnegative supermartingales

本文通过非负超鞅方法，统一并加强了多种鞅的尾界，提供了时间均匀集中性的最强大且通用的陈述。

关于某些相依增量过程的超越时间

On exceedance times for some processes with dependent increments

设${Z_n}_{n\ge 0}$是具有负漂移和i.i.d.的随机游动。增量的重尾分布，并让$M=\sup_{n\ge 0}Z_n$是它的上确界。Asmussen和Kl{ü}ppelberg（1996）考虑了随机游走的行为，给定$M>x$，对于$x$大，并获得了一个极限定理，作为$x\to\infty$，用于四元组的分布，包括超过水平$x$的时间$\rtreg=\rtreg(x)$，此时的位置$Z_{\rtreg}$，前一时间的位置$Z_{\rtreg-1}$，以及到达它的轨迹（对于Cramér-Lundberg保险风险过程也得到了类似的结果）。我们在这里得到几个扩展的结果，各种再生型模型，特别是与依赖增量的随机游走的情况下。特别注意描述的限制条件行为的$τ$。这类模型包括马尔可夫调制模型作为特殊情况。我们还研究了流体模型，Bj{<$}rk-Grandell风险过程，给出了$τ$的顺序与随机游走情况真正不同的例子，并讨论了哪些增长率是可能的。我们的证明纯粹是概率性的，并且基于Asmussen，Schmidli & Schmidt（1999），Foss & Zachary（2002）和Foss，Konstantopoulos & Zachary（2007）的结果和想法。

Fluctuations of Transverse Increments in Two-dimensional First Passage Percolation

We consider a model of first passage percolation (FPP) where the nearest-neighbor edges of the standard two-dimensional Euclidean lattice are equipped with random variables. These variables are i.i.d.\, nonnegative, continuous, and have a finite moment generating function in a neighborhood of $0$. We derive consequences about transverse increments of passage times, assuming the model satisfies certain properties. Approximately, the assumed properties are the following: We assume that the standard deviation of the passage time on scale $r$ is of some order $σ(r)$, and $\left\{σ(r), r > 0\right\…