A Feynman-Kac approach to a paper of Chung and Feller on fluctuations in the coin-tossing game. (English) Zbl 1498.60304
The goal of this paper is to give a simple expression for the quantities \(P (N_{2n+1} = r)\), where \(N_n\) is the number of “positive” terms among \(S_1,S_2, \dots ,S_n\) (which arising in a fair coin-tossing game), and which seem to be not found in the literature.
This result is obtained by adapting the Feynman-Kac methodology and it extends some classical result of K. L. Chung and W. Feller [Proc. Natl. Acad. Sci. USA 35, 605–608 (1949; Zbl 0037.36310)].
This result is obtained by adapting the Feynman-Kac methodology and it extends some classical result of K. L. Chung and W. Feller [Proc. Natl. Acad. Sci. USA 35, 605–608 (1949; Zbl 0037.36310)].
Reviewer: Romeo Negrea (Timişoara)
MSC:
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
| 60J65 | Brownian motion |
| 81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |
Citations:
Zbl 0037.36310References:
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