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A Theorem on Gambling Systems for Arbitrary Sequences of Random Variables
Author(s) -
Wen Liu
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609399005913
Subject(s) - mathematics , bernoulli's principle , random variable , martingale (probability theory) , bernoulli distribution , convergence of random variables , martingale difference sequence , convergence (economics) , moment (physics) , bernoulli process , moment generating function , discrete mathematics , pure mathematics , statistics , physics , classical mechanics , economic growth , engineering , economics , aerospace engineering
A theorem on gambling systems for Bernoulli sequences is extended to arbitrary sequences of random variables by using the notion of the likelihood ratio, and the martingale technique together with the tool of moment generating functions for the study of a.e. convergence is presented. 1991 Mathematics Subject Classification 60F99.