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Sojourn time in ℤ+ for the Bernoulli random walk on ℤ

Aimé Lachal — 2012

ESAIM: Probability and Statistics

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 distribution....

Cyclic random motions in d -space with directions

Aimé Lachal — 2006

ESAIM: Probability and Statistics

We study the probability distribution of the location of a particle performing a cyclic random motion in d . The particle can take possible directions with different velocities and the changes of direction occur at random times. The speed-vectors as well as the support of the distribution form a polyhedron (the first one having constant sides and the other expanding with time ). The distribution of the location of the particle is made up of two components: a singular component (corresponding to...

Sojourn time in ℤ for the Bernoulli random walk on ℤ

Aimé Lachal — 2012

ESAIM: Probability and Statistics

Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters p ∈ (0,1) and q = 1 − p. 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...

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