Non-classical law of the iterated logarithm behaviour for trimmed sums

DOI10.1007/BF00322025zbMath0643.60026MaRDI QIDQ1102031

Philip S. Griffin

Publication date: 1988

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

trimmed sumslaw to time t. Assuming a stability condition on the drift and boundedness of the diffusion matrix, we derive an a priori estimate for this supremum, logarithmically increasing in time. Moreover, the rate of increase is shown to be optimal

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

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Cites Work

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• Approximate local limit theorems for laws outside domains of attraction
• Extreme values and the law of the iterated logarithm
• The influence of extremes on the law of the iterated logarithm
• General one-sided laws of the iterated logarithm
• Laws of the iterated logarithm for sums of the middle portion of the sample
• Relative stability of trimmed sums
• An Interpretation of the Finite Mean LIL Norming Constants
• The 1971 Rietz Lecture Sums of Independent Random Variables--Without Moment Conditions

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