Law of iterated logarithm for markov chains in markovian environments
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The law of iterated logarithm of
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Precise asymptotic in the laws of large numbers and law of iterated logarithm for some statistics
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It is an extension of " the law of iterated logarithm of kolmogorov " . in the course of proving , we extend two lemmas and use the relating results of partial sum increment of independent r . v
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We have been familiar with " the law of iterated logarithm of kolmogorov " and " the law of iterated logarithm of hartman - wintner " . this paper will mainly discuss the law of iterated logarithm for some kind weighted partial sum
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As for i . i . d . r . v . , we get the extension of " the law of iterated logarithm of hartman - wintner " under weaker conditions . at the end of this paper , we discuss that the moment conditions of theorem are necessary to the law of iterated logarithm of this form
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Let { xn ; n > 1 } be mutually identically independent random variables distributed according to the normal distribution , { sn , n > 1 } be finite partial sum series , the purpose of this paper is to investigate law of the iterated logarithm type results for special finite partial weight sum series { sn , n > 1 } , we assume that sn = a1sn + a2 ( s2n - sn ) + a3 ( s3n - s2n ) + . . . + ad ( sdn - s ( d - 1 ) n ) in the second chapter , theory 2 by using the method of literature [ 8 ] , we extend hartman - wintner law of iterated logarithm on the gauss distribution . we substitute negative correspond for independent . it extends the corresponding results in gauss distribution
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