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A Note on Planar Random Motion at Finite Speed

  • Alexander D. Kolesnik (a1)

Abstract

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.

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Copyright

Corresponding author

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

References

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Courant, R. and Gilbert, D. (1962). Methods of Mathematical Physics, Vol 2, Partial Differential Equations. Interscience, New York.
John, F. (1955). Plane Waves and Spherical Means Applied to Partial Differential Equations. Interscience, New York.
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, 11681182.
Masoliver, J., Porrá, J. M. and Weiss, G. H. (1993). Some two and three-dimensional persistent random walks. Physica A 193, 469482.
Stadje, W. (1987). The exact probability distribution of a two-dimensional random walk. J. Statist. Phys. 46, 207216.
Stadje, W. (1989). Exact probability distributions for non-correlated random walk models. J. Statist. Phys. 56, 415435.
Vladimirov, V. S. (1981). The Equations of Mathematical Physics. Nauka, Moscow.

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