Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T09:42:28.272Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Planar Random Motion at Finite Speed

Part of:Stochastic analysisMarkov processesNonparametric inferenceSpecial processes

Published online by Cambridge University Press:  14 July 2016

Alexander D. Kolesnik
Alexander D. Kolesnik*
Affiliation:
Academy of Sciences of Moldova
*
∗ Postal address: Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academy Street 5, Kishinev, MD-2028, Moldova. Email address: kolesnik@math.md
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A simple derivation of the explicit form of the transition density of a planar random motion at finite speed, based on some specific properties of the wave propagation on the plane R 2, is given.

Keywords

Random motionfinite speedrandom evolutionexplicit probability lawwave propagationwave diffusionwave equationfundamental solutionHuygens principle

MSC classification

Secondary:60K99: None of the above, but in this section62G30: Order statistics; empirical distribution functions60K35: Interacting random processes; statistical mechanics type models; percolation theory60J60: Diffusion processes60H30: Applications of stochastic analysis (to PDE, etc.)

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007, pp. 838 - 842
Copyright
Copyright © Applied Probability Trust 2007 

References

Courant, R. and Gilbert, D. (1962). Methods of Mathematical Physics, Vol 2, Partial Differential Equations. Interscience, New York.Google Scholar
John, F. (1955). Plane Waves and Spherical Means Applied to Partial Differential Equations. Interscience, New York.Google Scholar
Kolesnik, A. D. and Orsingher, E. (2005). A planar random motion with an infinite number of directions controlled by the damped wave equation. J. Appl. Prob. 42, 1168–1182.Google Scholar
Masoliver, J., Porrá, J. M. and Weiss, G. H. (1993). Some two and three-dimensional persistent random walks. Physica A 193, 469–482.Google Scholar
Stadje, W. (1987). The exact probability distribution of a two-dimensional random walk. J. Statist. Phys. 46, 207–216.Google Scholar
Stadje, W. (1989). Exact probability distributions for non-correlated random walk models. J. Statist. Phys. 56, 415–435.Google Scholar
Vladimirov, V. S. (1981). The Equations of Mathematical Physics. Nauka, Moscow.Google Scholar