scholarly journals An almost sure invariance principle for Hilbert space valued martingales

1982 ◽  
Vol 273 (1) ◽  
pp. 231-231 ◽  
Author(s):  
Gregory Morrow ◽  
Walter Philipp
Keyword(s):  
Hilbert Space ◽  
Invariance Principle ◽  
Almost Sure Invariance Principle

scholarly journals Almost sure invariance principle for some maps of an interval

1985 ◽  
Vol 5 (4) ◽  
pp. 625-640 ◽  
Author(s):  
Krystyna Ziemian
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Critical Points ◽  
Measurable Function ◽  
Schwarzian Derivative ◽  
Almost Sure Invariance Principle

AbstractWe prove an almost sure invariance principle and a central limit theorem for the process , where f is a map of an interval with a non-positive Schwarzian derivative whose trajectories of critical points stay far from the critical points, and F is a measurable function with bounded p-variation (p ≥ 1).The almost sure invariance principle implies the Log-log laws, integral tests and a distributional type of invariance principle for the process .

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