Renewal Theorems for Markov Chains
Abstract
This study originated in an attempt to understand the meaning of two parameters, the mean and the variance, which appear in the limit theorems concerning sums of identically distributed independent random variables. The law of large numbers, when written in the usual form (lim Sn/n = micrometer) does not immediately suggest a natural generalization to Markov chains; the reason is that a Markov chain takes its values in an abstract state space so that not only the limit micrometer, but also the ratios which tend to micrometer have to be reinterpreted in a meaning-ful fashion. Therefore, we proceed to the renewal theorem in the form proved by Erdos, Feller, and Pollard (cf. [3], p. 286) and Chung and Wolfowitz [2], and formulate it in a manner which readily suggests a natural generalization.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1967
- Accession Number
- AD1027218
Entities
People
- F. Spitzer
Organizations
- Cornell University