Asymptotic Expansions for Large Deviation Probabilities in the Strong Law of Large Numbers.
Abstract
Let X sub 1, X sub 2,...be a sequence of independent random variables with common distribution function F having zero mean, and let (S sub n) be the random walk of partial sums. The weak and strong laws of large numbers, respectively, imply that for any alpha epsilon IR and epsilon > O the probabilities P(S sub m > alpha + epsilon m) and P sub m = P(S sub n > alpha + epsilon n for some n > or = m) tend to 0 as m tends to infinity. Building upon work of Bahadur and Ranga Rao, The author produces complete asymptotic expansions for the probabilities P(S sub m > alpha + epsilon m) and P sub m.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1987
- Accession Number
- ADA187432
Entities
People
- James A. Fill
Organizations
- Stanford University