Abstract
While the general principles involved in the formulation of random walk and Brownian motion equations (whether the random changes are directly on the position of a particle or individual, or on the velocity) are well-known, there are various situations considered in the literature involving the assumption of a constant speed (in magnitude). Thus the derivation by Goldstein (1951) of a one-dimensional wave-like equation involved the tacit assumption Ut = ± a, where Ut is the vector velocity dRt/dt,Rt being the (column) position vector (Bartlett (1957)). Biological models may involve the assumption of individuals moving at constant speed (cf. Kendall (1974)). Finally, the derivation of Schrodinger-type equations from Brownian motion models has sometimes involved the assumption U′tUt = c2, where c is the velocity of light (Cane (1967), (1975)).
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference6 articles.
1. Kendall D. G. (1974) Pole-seeking Brownian motion and bird navigation. J.R. Statist. Soc. B 36, 365–417.
2. Some problems associated with random velocity;Bartlett;Publ. Inst. Statist. Univ. Paris,1957
3. Random walks and physical processes;Cane;Bull. Internat. Statist. Inst.,1967
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