Law of the iterated logarithm for solutions of stochastic equations
نویسندگان
چکیده
منابع مشابه
Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm , with Applications to Financial Markets ∗
By using a change of scale and space, we study a class of stochastic differential equations (SDEs) whose solutions are drift–perturbed and exhibit asymptotic behaviour similar to standard Brownian motion. In particular sufficient conditions ensuring that these processes obey the Law of the Iterated Logarithm (LIL) are given. Ergodic–type theorems on the average growth of these non-stationary pr...
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The law of the iterated logarithm provides a family of bounds all of the same order such that with probability one only finitely many partial sums of a sequence of independent and identically distributed random variables exceed some members of the family, while for others infinitely many do so. In the former case, the total number of such excesses has therefore a proper probability distribution...
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Let [Formula: see text] be a stationary LNQD sequence of random variables with zero means and finite variance. In this paper, by the Kolmogorov type maximal inequality and Stein's method, we establish the result of the law of the iterated logarithm for LNQD sequence with less restriction of moment conditions. We also prove the law of the iterated logarithm for a linear process generated by an L...
متن کاملThe Law of the Iterated Logarithm for p-Random Sequences
The stochastic properties of p-random sequences are studied in this paper. It is shown that the law of the iterated logarithm holds for p-random sequences. This law gives a quantitative characterization of the density of p-random sets. When combined with the invari-ance property of p-random sequences, this law is also useful in proving that some complexity classes have p-measure 0.
متن کاملThe law of the iterated logarithm for character ratios
Recently, Fulman developed some general connections between martingales and character ratios of a random representation of the symmetric group on transitions, and obtained a convergence rate in a central limit theorem. In this work we aim to establish the law of the iterated logarithm for character ratios. The technique is a well-known Skorokhod embedding theorem for martingales and strong appr...
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ژورنال
عنوان ژورنال: Theory of Probability and Mathematical Statistics
سال: 2011
ISSN: 0094-9000,1547-7363
DOI: 10.1090/s0094-9000-2012-00840-5