Singles in a Markov chain

Abstract:

Let {Xi, i ≥ 1} denote a sequence of variables that take values in {0, 1} and suppose that the sequence forms a Markov chain with transition matrix P and with initial distribution (q, p) = (P(X1 = 0), P(X1 = 1)). Several authors have studied the quantities Sn, Y (r) and AR(n), where Sn = ∑i=1n Xi denotes the number of successes, where Y (r) denotes the number of experiments up to the r-th success and where AR(n) denotes the number of runs. In the present paper we study the number of singles AS(n) in the vector (X1,X'2, . . . , Xn). A single in a sequence is an isolated value of 0 or 1, i.e., a run of length 1. Among others we prove a central limit theorem for AS(n).

Año de publicación:

2008

Keywords:

Fuente:

scopus