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A limit theorem for partial sums of random variables and its applications

✍ Scribed by Wen Liu; Jia-an Yan; Weiguo Yang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
131 KB
Volume
62
Category
Article
ISSN
0167-7152

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✦ Synopsis

In this paper, we establish a new limit theorem for partial sums of random variables. As corollaries, we generalize the extended Borel-Cantelli lemma, and obtain some strong laws of large numbers for Markov chains as well as a generalized strong ergodic theorem for irreducible and positive recurrent Markov chains.

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The random variables (r.vs.) X , . i E S : = ( 1 , 2 ...I, to he dealt uith are measurable mappings from a probability space (9. 91, P ) into a measure space (B, %), R being a RANACH space with a countable hasis (e,),,,, and ' 3 the o-algebra of 13orel sets of B. The type of convergence to be mainly