Shooting randomly against a line in Euclidean and non-Euclidean spaces

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-01-02 DOI:10.1080/17442508.2012.749260

E. Orsingher, Bruno Toaldo

引用次数: 0

Abstract

In this paper we study a class of distributions related to the r.v. , for different distributions of . The problem is related to the hitting point of a randomly oriented ray and generalizes the Cauchy distribution in different directions. We show that the distribution of solves the Laplace equation of order , possesses even moments of order , and has bimodal structure when is uniform. We study also a number of distributional properties of functionals of , including those related to the arcsine law. Finally we study the same problem in the Poincaré half-plane and this leads to the hyperbolic distribution of which the main properties are explored. In particular we study the distribution of hyperbolic functions of , the law of sums of i.i.d. r.v.'s and the distribution of the area of random hyperbolic right triangles.

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在欧几里得和非欧几里得空间中对着一条线随机射击

本文研究了一类与rv有关的分布，对于的不同分布。该问题涉及随机定向射线的命中点，并在不同方向上推广柯西分布。证明了该分布解有序拉普拉斯方程，具有偶阶矩，且在均匀时具有双峰结构。我们还研究了泛函的一些分布性质，包括与反正弦律有关的性质。最后，我们在庞卡罗半平面上研究了同样的问题，得到了双曲分布，并探讨了双曲分布的主要性质。特别地，我们研究了双曲函数的分布，i.i.r.v.的和律。和随机双曲直角三角形的面积分布。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.