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Convergence of transport processes with radially symmetric direction changes, and chain molecules

Published online by Cambridge University Press:  14 July 2016

Luis G. Gorostiza
Luis G. Gorostiza*
Affiliation:
Centro de Investigación del IPN, México D. F.
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Abstract

When passing from two to more dimensions, the study of non-isotropic scattering transport processes, and chain molecules, which are both covered by the same mathematical model, becomes affected by the non-commutativity of rotations. The techniques developed in [2], together with results on radially symmetric direction changes, are used in this paper to obtain a functional central limit theorem for those random processes, with a suitable normalization, the limit being a Brownian motion process which is completely identified.

Keywords

WEAK CONVERGENCEBROWNIAN MOTIONTRANSPORT PROCESSCHAIN MOLECULEEYRING FORMULA
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 812 - 816
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Cogburn, R. and Hersh, R. (1973) Two limit theorems for random differential equations, Indiana Univ. Math. J. 22, 1067–1089.CrossRefGoogle Scholar
[2] Gorostiza, L. G. (1973) An invariance principle for a class of d-dimensional polygonal random functions. Trans. Amer. Math. Soc. 177, 413–445.Google Scholar
[3] Ito, K. and Mckean, H. P. (1965) Diffusion Processes and their Sample Paths. Springer-Verlag, New York.Google Scholar
[4] Kac, M. (1959) Probability and related topics in physical sciences. Lectures in Appl. Math. Vol. 1, Interscience, New York.Google Scholar
[5] Khas'Minskii, R. Z. (1966) A limit theorem for the solution of differential equations with random right-hand sides. Theor. Prob. Appl. 9, 390–406.CrossRefGoogle Scholar
[6] Papanicolaou, G. C. and Varadhan, S. R. S. (1973) A limit theorem with strong mixing in Banach space and two applications to stochastic differential equations. Comm. Pure Appl. Math. 26, 497–524.Google Scholar
[7] Watanabe, S. and Watanabe, T. (1970) Convergence of isotropic scattering transport process to Brownian motion. Nagoya Math. J. 40, 161–171.Google Scholar