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A Feynman–Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game
- Source :
- Proceedings of the American Mathematical Society. 150:4027-4036
- Publication Year :
- 2022
- Publisher :
- American Mathematical Society (AMS), 2022.
-
Abstract
- A classical result of K. L. Chung and W. Feller deals with the partial sums S k S_k arising in a fair coin-tossing game. If N n N_n is the number of “positive” terms among S 1 S_1 , S 2 S_2 , …, S n S_n then the quantity P ( N 2 n = 2 r ) 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 2 n + 1 = r ) P(N_{2n+1} = r) , r = 0 r = 0 , 1 1 , 2 2 , …, 2 n + 1 2n+1 . We get to this ansatz by adaptating the Feynman–Kac methodology.
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 150
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi...........eae6aecfb954c9adfa60c9ee247d4e95