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Velocity of stochastic processes in two dimensions

Published online by Cambridge University Press:  01 July 2016

Denis Mollison
Denis Mollison*
Affiliation:
Heriot-Watt University
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Extract

A basic class of spatial stochastic processes is that in which the phenomenon spreads between static individuals with probability of ‘infection’ falling off with distance according to a contact distribution (Mollison (1972)). The following questions then arise:

(1) How does the velocity of spread depend on the contact distribution? In particular, for which contact distributions is it finite?

(2) Does the phenomenon spread at a steady velocity, or does it spread in jumps?

Type
Stochastic Modelling
Information
Advances in Applied Probability , Volume 7 , Issue 3 , September 1975 , pp. 458 - 459
Copyright
Copyright © Applied Probability Trust 1975 

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References

Hammersley, J. M. (1966) First-passage percolation. J. R. Statist. Soc. B 28, 491–496.Google Scholar
Mollison, D. (1972) The rate of spatial propagation of simple epidemics. Proc. 6th Berk. Symp. Math. Statist. Prob. 3, 579–614.Google Scholar
Mollison, D. (1974) Velocity of stochastic processes in two dimensions. Proc. 1974 European Meeting of Statisticians, Prague. To appear.Google Scholar
Richardson, D. (1973) Random growth in a tesselation. Proc. Camb. Phil. Soc. 74, 515–528.CrossRefGoogle Scholar