| Description |
1 online resource (145 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 2, issue 2, number 161 (July 1975) |
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Memoirs of the American Mathematical Society ; no. 161.
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| Contents |
Introduction -- Description of the method -- Lacunary trigonometric series with unweighted summands -- Stationary [capital Greek] Phi-mixing sequences -- Gaussian sequences -- Lacunary trigonometric series with weights -- Functions of strongly mixing random variables -- Nonstationary mixing sequences -- A refinement of the Shannon-McMillan-Breiman theorem -- Markov sequences -- Retarded asymptotic martingale difference sequences -- Continuous parameter stochastic processes -- Appendix 1. The Gaal-Koksma strong law of large numbers -- Appendix 2. An example |
| Summary |
A strong revival of interest in the law of the iterated logarithm and related asymptotic fluctuation results has occurred in the last decade, stimulated by two remarkable papers by Volker Strassen. In these papers, Strassen introduces a new method for establishing such fluctuation results for sums of independent random variables and for martingales. Strassen's almost sure invariance principle for martingales states that each martingale satisfying a certain second moment condition is with probability on "close" to a Brownian motion. In this monograph we investigate the asymptotic fluctuation behavior of sums of weakly dependent random variables, such as lacunary trigonometric mixing, and Gaussian sequences |
| Notes |
"Volume 2, issue 2." |
| Bibliography |
Includes bibliographical references (pages 138-140) |
| Notes |
English |
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Print version record |
| Subject |
Random variables.
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Partial sums (Series)
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Sequences (Mathematics)
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Stochastic processes.
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Stochastic Processes
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Partial sums (Series)
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Random variables
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Sequences (Mathematics)
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Stochastic processes
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| Form |
Electronic book
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| Author |
Stout, William F., 1940- author.
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| ISBN |
9781470405472 |
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1470405474 |
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