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arXiv · 1810.06092

A Feyman-Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game

F. Alberto Grünbaum
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Abstract

A classical result of K. L. Chung and W. Feller deals with the partial sums $S_k$ arising in a fair coin-tossing game. If $N_n$ is the number of "positive" terms among $S_1, S_2,\dots,S_n$ then the quantity $P(N_{2n}=2r)$ takes an elegant form. We lift the restriction on an even number of tosses and give a simple expression for $P(N_{2n+1}=r)$, $r=0,1,2,\dots,2n+1$. We get to this result by adapting the Feynman-Kac methodology.

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F. Alberto Grünbaum. 2018-10-14. A Feyman-Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game. https://arxiv.org/abs/1810.06092

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