Sojourn time in ℤ+ for the Bernoulli random walk on ℤ
Aimé Lachal (2012)
ESAIM: Probability and Statistics
Similarity:
Let (S) be the classical Bernoulli random walk on the integer line with jump parameters ∈ (01) and = 1 − . The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [35 (1949) 605–608], simpler representations may be obtained for its probability...