Results 1 to 10 of about 177,430,963 (194)

Precise Asymptotics in the Law of Iterated Logarithm for Moving Average Process under Dependence

Journal of Inequalities and Applications, 2011
Let be a doubly infinite sequence of identically distributed and -mixing random variables, and let be an absolutely summable sequence of real numbers.
Jie Li
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On the uniqueness of higher order Gubinelli derivatives and an analogue of the Doob – Meyer theorem for rough paths of the arbitrary positive Holder index

Журнал Белорусского государственного университета: Математика, информатика, 2022
In this paper, we investigate the features of higher order Gubinelli derivatives of controlled rough paths having an arbitrary positive Holder index. There is used a notion of the (α, β)-rough map on the basis of which the sufficient conditions are given
Maksim M. Vaskovskii
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Laws of the iterated logarithm for iterated perturbed random walks

Modern Stochastics: Theory and Applications
Let ${({\xi _{k}},{\eta _{k}})_{k\ge 1}}$ be independent identically distributed random vectors with arbitrarily dependent positive components and ${T_{k}}:={\xi _{1}}+\cdots +{\xi _{k-1}}+{\eta _{k}}$ for $k\in \mathbb{N}$. The random sequence ${({T_{k}}
Oksana Braganets
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The law of the iterated logarithm on subsequences-characterizations [PDF]

Nagoya Mathematical Journal, 1990
Let be any increasing sequence of integers and M> 1; we connect to them in a very simply way, an increasing unbounded function φ: → R+. Let also X1, X2, · · · be a sequence of i.i.d. random vectors with value in euclidian space Rm. We prove that the cluster set of the sequence almost surely coincides with the unit ball of Rm, if, and only if, the ...
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A Generalization of Kolmogorov's Law of the Iterated Logarithm [PDF]

Proceedings of the American Mathematical Society, 1972
A version of the law of the iterated logarithm is proved for sequences of independent random variables which satisfy the central limit theorem in such a way that the convergence of the appropriate moment-generating functions to that of the standard normal distribution occurs at a particular rate.
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A general law of the iterated logarithm for non-additive probabilities

Results in Applied Mathematics
Motivated by some interesting problems in mathematical economics, quantum mechanics and finance, non-additive probabilities have been used to describe the phenomena which are generally non-additive. In this paper, we further study the law of the iterated
Zhaojun Zong, Miaomiao Gao, Feng Hu
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Exponential Inequalities for Positively Associated Random Variables and Applications

Journal of Inequalities and Applications, 2008
We establish some exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira (2005).
Ailin Liu, Shanchao Yang, Guodong Xing
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On the Multivariate Law of the Iterated Logarithm

The Annals of Probability, 1979
A Hilbert space law of the iterated logarithm is proved which generalizes Kolmogorov's law for bounded random variables and which generalizes results of Teicher for unbounded random variables. The result for identically distributed random vectors is a consequence.
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On the Law of the Iterated Logarithm for Martingales

The Annals of Probability, 1992
Let \(\{U_n\), \(n\geq 1\}\) be a martingale adapted to an increasing sequence of \(\sigma\)-fields \(\{\mathcal F_n\), \(n\geq 1\}\) and \(s_n^2 = \sum_{i=1}^n E(X_i^2\mid\mathcal F_{i-1})\), \(n\geq 1\). The main result establishes (with probability 1) an upper bound of \(\limsup_{n\to\infty}U_n/s_n\varphi(s_n)\) with \(\varphi(x):=(2\log\log(x^2\vee
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General Convergence Rates by the Delayed Sums Method

Axioms
In this study, we propose a delayed sums method to investigate the convergence rates of partial sums. This approach enables general and systematic treatment of the convergence behavior of partial sums, encompassing and extending classical results such as
Cheng Hu, Shangshang Yang, Tonghui Wang
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