Limit Theorems for “Random Flights”

被引：0

作者：

Davydov Y.A. ^{[1
,2
]}

机构：

[1] St. Petersburg State University, St. Petersburg

[2] Université de Lille, Lille

来源：

Journal of Mathematical Sciences | 2023年 / 273卷 / 5期

关键词：

D O I：

10.1007/s10958-023-06538-3

中图分类号：

学科分类号：

摘要：

The article discusses the asymptotic behavior of a particle performing so-called “random flight.” In a recent work by Davydov–Konakov (2017), when the moments Tk of changing the direction of the particle form an inhomogeneous Poisson process, it was shown that, depending on the nature of the inhomogeneity, three variants of the limiting distribution arise naturally for the zoomed particle trajectory. The purpose of this work is to show that these three options are preserved under much more general assumptions about the sequence (Tk). © 2023, Springer Nature Switzerland AG.

引用

页码：755 / 762

页数：7

共 10 条

[1]

Billingsley P., Convergence of Probability Measures, (1968)

[2]

Davydov Y., Konakov V., ”Random walks in non homogeneous Poisson environment, Modern Problems of Stochastic Analysis and Statistics – Selected Contributions in Honor of V. Konakov, 208, pp. 3-24, (2017)

[3]

Gikhman I.I., Skorohod A.V., Introduction to the Theory of Random Processes, (1996)

[4]

Kluyver J.C., ”A local probability problem, Proceedings of the Section of Sciences, Koninklijke Akademie Van Wetenschappen Te Amsterdam, 8, pp. 341-350, (1905)

[5]

Mandelbrot B., The Fractal Geometry of Nature, (1982)

[6]

Orsingher E., Garra R., Random flights governed by Klein–Gordon type partial differential equations, Stoch. Proc. Appl., 124, pp. 2171-2187, (2014)

[7]

Pearson K., ”The problem of the Random Walk, Nature, 72, (1905)

[8]

Rayleigh L., On the problem of the random flights and of random vibrations in one, two and three dimensions, Philosophical Magazine, 37, pp. 321-347, (1919)

[9]

Vysotsky V.V., ”A limit theorem for the position of a particle in the Lorentz model, ”J. Math. Sci., 139, 3, pp. 6520-6534, (2006)

[10]

Vysotsky V.V., A functional limit theorem for the position of a particle in a Lorentz type model, Markov Processes and Related Fields, 12, 4, pp. 767-790, (2007)

← 1 →