An Identity for Two Integral Transforms Applied to the Uniqueness of a Distribution via its Laplace-Stieltjes Transform

A finite difference approach to the infinity Laplace equation and tug-of-war games

We present a modified version of the two-player "tug-of-war" game introduced by Peres, Schramm, Sheffield, and Wilson. This new tug-of-war game is identical to the original except near the boundary of the domain $\partial Ω$, but its associated value functions are more regular. The dynamic programming principle implies that the value functions satisfy a certain finite difference equation. By studying this difference equation directly and adapting techniques from viscosity solution theory, we prove a number of new results. We show that the finite difference equation has unique maximal and minim…

超线性输运噪声驱动的分数阶随机p-拉普拉斯方程的适定性

Well-posedness of Fractional Stochastic p-Laplace Equations Driven by Superlinear Transport Noise

本文针对超线性输运噪声驱动的分数阶随机p-拉普拉斯方程，通过单调方法证明抽象方程解的存在唯一性，结合伽辽金近似与拓扑空间上的表示定理，解决近似解序列的 tightness 和一致可积性问题，得到原方程解的存在唯一性。

An extension of Hewitt's inversion formula and its application to fluctuation theory

We analyze fluctuations of random walks with generally distributed increments. Integral representations for key performance measures are obtained by extending an inversion theorem of Hewitt [11] for Laplace-Stieltjes transforms. Another important part of the anal- ysis involves the so-called harmonic measures associated to the distribution of the increment of the walk. It is also pointed out that such representations can be explicitly calculated, if one assumes a form of rational structure for the increment transform. Applications include, but are not restricted to, queueing and insurance risk…

双重变换Tauberian方法用于精确的大偏差分析

Double-transform Tauberian method for precise large deviations

本文提出了一种双重变换Tauberian方法，用于研究具有相关增量或路径约束的随机过程的大偏差，扩展了之前针对单变量Laplace-Stieltjes变换的精确大偏差方法到双变量情形，为分析大偏差提供了直接途径。

无穷可分的修正贝塞尔分布

Infinitely divisible modified Bessel distributions

本文研究支持在[0,∞)上的连续单变量概率分布（如McKay分布、K分布、广义逆高斯分布和广义McKay分布），证明它们属于无穷可分分布、自可分解分布、广义伽马卷积和双曲完全单调密度类，并通过特殊函数技术给出新证明，推导出修正贝塞尔函数乘积和商的新Stieltjes变换表示，从而获得新的无穷可分修正贝塞尔分布。

Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable

We give a sufficient condition for the exponential decay of the tail probability of a non-negative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a theorem, according to which if the abscissa of convergence of the LS transform is negative finite and the real point on the axis of convergence is a pole of the LS transform, then the tail probability decays exponentially. For the proof of the theorem, we extend and apply so-called a finite form of Ikehara's complex Tauberian theorem by Graham-Vaaler.

Absolute moments in terms of characteristic functions

The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the characteristic function (which have been ignored in the literature) and provide some new results as well. The case of nonnegative random variables is also investigated through both characteristic function and Laplace-Stieltjes transform. Besides, we prove that the distribution of a nonnegative random variable with a finite fractional moment can be completely …

通过一致Tauber型定理的精确大偏差

Precise large deviations through a uniform Tauberian theorem

通过证明Laplace-Stieltjes变换的一致Tauber型定理，为谱正稳定分布吸引域中的随机变量族推导大偏差原理，该方法可处理现有技术难以解决的随机游走长程记忆核和随机停时和等情形。