A limit property of random conditional probabilities

✍ Scribed by Wen Liu

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 83 KB
• Volume: 49
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(00)00061-4

✦ Synopsis

Let {Xn; n¿0} be a sequence of random variables taking values in S = {1; 2; : : : ; N }, and let p k (x k | x0; : : :

In this paper a theorem on a.e. convergence for the harmonic mean of the random conditional probabilities {p k (X k | X0; : : : ; X k-1 ); 16k6n} is obtained by using the tool of the conditional moment generating function and the di erentiation on a net.