The Functional Law of the Iterated Logarithm for Stationary Strongly Mixing Sequences
نویسندگان
چکیده
منابع مشابه
Law of the Iterated Logarithm for Stationary Processes
There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes · · ·X−1, X0, X1, · · · whose partial sums Sn = X1 + · · · + Xn are of the form Sn = Mn+Rn, where Mn is a square integrable martingale with stationary increments and Rn is a remainder term for which E(R 2 n) = o(n). Here we explore the Law of the Iterated Logarithm (LIL) for the...
متن کاملThe law of the iterated logarithm for LNQD sequences
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 کاملChover-type laws of the k -iterated logarithm for weighted sums of strongly mixing sequences
This note contains a Chover-type Law of the k -Iterated Logarithm for weighted sums of strong mixing sequences of random variables with a distribution in the domain of a stable law. We show that the upper part of the LIL is similar to other studies in the literature; conversely, the lower half is substantially different. In particular, we show that, due to the failure of the classical version o...
متن کاملOn the law of the iterated logarithm.
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1995
ISSN: 0091-1798
DOI: 10.1214/aop/1176988179