Abstract
It is well known in random walk theory that the probability of a return to the origin at epoch 2n equals the probability of no return to the origin. Quite satisfying algebraic proofs exist, but Feller has popularised geometrical proofs which snip, reflect and slide portions of the graph of the random walk. We here suggest improved versions of two such proofs.
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References
W. Feller, An Introduction to Probability Theory and its Applications, Volume I (John Wiley and Sons, New York, London, Sydney, 1970).
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© 1975 Springer-Verlag
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Doherty, M. (1975). An amusing proof in fluctuation theory. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069549
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DOI: https://doi.org/10.1007/BFb0069549
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