A limit property of random conditional probabilities

Wen Liu

Statistics & Probability Letters, 2000, vol. 49, issue 3, 299-304

Abstract: Let {Xn,n[greater-or-equal, slanted]0} be a sequence of random variables taking values in S={1,2,...,N}, and let pk(xk x0,...,xk-1)=P(Xk=xk X0=x0,...,Xk-1=xk-1). In this paper a theorem on a.e. convergence for the harmonic mean of the random conditional probabilities {pk(Xk X0,...,Xk-1), 1[less-than-or-equals, slant]k[less-than-or-equals, slant]n} is obtained by using the tool of the conditional moment generating function and the differentiation on a net.

Keywords: Random; conditional; probability; Conditional; moment; generating; function; Strong; limit; theorem; Harmonic; mean; Differentiation; on; a; net (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (1)

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