Some exact distributions of the number of one-sided deviations and the time of the last such deviation in the simple random walk

Chern-Ching Chao and John Slivka

Stochastic Processes and their Applications, 1987, vol. 24, issue 2, 279-286

Abstract: For every positive integer n, let Sn be the n-th partial sum of a sequence of independent and identically distributed random variables, each assuming the values +1 and -1 with respective probabilities p (0 ([mu] + [lambda])n [Sn[greater-or-equal, slanted]([mu] + [lambda])n] and let L+[L*] be the supremum of the values of n for which Sn > ([mu] + [lambda])n [Sn[greater-or-equal, slanted]([mu] + [lambda])n], where sup Oslash; = 0. Explicit expressions for the exact distributions of N+, N*, L+ and L* are given when [mu] + [lambda] = ±k/(k + 2) for any nonnegative integer k.

Keywords: strong; law; of; large; numbers; sums; of; i.i.d.; Bernoulli; variables; linear; boundary; crossings; number; of; exits; last; exit; time (search for similar items in EconPapers)
Date: 1987
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