A Continuous Analogue of the Invariance Principle and Its Almost Sure Version
نویسنده
چکیده
Abstract. We deal with random processes obtained from a homogeneous random process with independent increments by replacement of the time scale and by multiplication by a norming constant. We prove the convergence in distribution of these processes to Wiener process in the Skorohod space endowed by the topology of uniform convergence. An integral type almost sure version of this limit theorem is obtained. 2000 AMS Mathematics Subject Classification. 60F05 Central limit and other weak theorems, 60F15 Strong theorems.
منابع مشابه
AN ALMOST SURE INVARIANCE PRINCIPLE FOR THE EXTREMA OF CERTAIN SAMPLE FUNCTIONS By
For a general class of statistics expressible as extrema of certain sample functions, an almost sure invariance principle, particularly useful in the context of the law of iterated logarithm and the probabilities of moderate deviations, is established, and its applications are stressed . .~ AMS 1970 Classification Numbers: 60FlO, 60F15
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For a general class of statistics expressible as extrema of certain sample functions, an almost sure invariance principle, particularly useful in the context of the law of iterated logarithm and the probabilities of moderate deviations, is established, and its applications are stressed. AMS 1970 Classification Numbers: 60FlO, 60F15
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