Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T19:55:18.315Z Has data issue: false hasContentIssue false
  • English
  • Français

A planar random motion governed by the two-dimensional telegraph equation

Published online by Cambridge University Press:  14 July 2016

Enzo Orsingher
Enzo Orsingher*
Affiliation:
University of Rome
*
∗Postal address: Dipartimento di Statistica, Probabilità e Statistiche Applicate, Facoltà di Statistica, University of Rome ‘La Sapienza', 00185 Rome, Italy.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper a planar random motion governed by the two-dimensional telegraph equation is presented. It is proved that the particle performing motion is at any time t within a circle centred at the starting point and with radius . The explicit density of the particle position is obtained. Results concerning the trend of motion are also given.

Keywords

POISSON PROCESSELECTROMAGNETIC EQUATIONSBERNOULLI RANDOM VARIABLES
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 385 - 397
Copyright
Copyright © Applied Probability Trust 1986 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bartlett, M. S. (1957) Some problems associated with random velocity. Publ. Inst. Statist. Univ. Paris 6, 261–270.Google Scholar
[2] Bartlett, M. S. (1978) A note on random walks at constant speed. Adv. Appl. Prob. 10, 704–707.Google Scholar
[3] Cane, V. R. (1967) Random walks and physical processes. Bull. Internat. Statist. Inst. 42 (1), 622–640.Google Scholar
[4] Cane, V. R. (1975) Diffusion models with relativity effects. In Perspectives in Probability and Statistics, ed. Gani, J., Applied Probability Trust, Sheffield, 263–273.Google Scholar
[5] Goldstein, S. (1951) On diffusion by discontinuous movements and the telegraph equation. Quart. J. Mech. Appl. Math. 4, 129–156.Google Scholar
[6] Henderson, R., Renshaw, E. and Ford, D. (1984) A correlated random walk model for two-dimensional diffusion. J. Appl. Prob. 21, 233–246.Google Scholar
[7] Nelson, E. (1966) Derivation of the Schrödinger equation from Newtonian mechanics. Phys. Rev. 150, 1079–1085.Google Scholar
[8] Orsingher, E. (1985) Hyperbolic equations arising in random models. Stoch. Proc. Appl. 21.CrossRefGoogle Scholar