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Random motion and analytic continued fractions

Published online by Cambridge University Press:  24 October 2008

I. J. Good
I. J. Good
Affiliation:
25 Scott House Princess Elizabeth Way Cheltenham
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Extract

In a previous note (Good (7)) it was shown that there is an intimate connexion between Legendre polynomials and ‘trinomial’ random walks, that is walks on a one-dimensional lattice with the same probabilities p–1p0, p1 at each point of taking a step of – 1,0,1. The purpose of the present note is to point out that if the probabilities depend on the current position of the particle, then there is scope for applications of the theory of analytic continued fractions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 1 , January 1958 , pp. 43 - 47
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

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