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Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors
partial hyperbolicity singular-hyperbolicity recurrence decay of correlations local dimension hitting times
2012/4/23
We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue...
A New Formula for the Natural Logarithm of a Natural Number
Natural Logarithm Natural Number Classical Analysis and ODEs
2011/9/20
Abstract: For every natural number $T,$ we write $\Ln T$ as a series, generalizing the known series for $\Ln 2.$.
Heuristic formula for logarithm of the Frobenius morphism
Heuristic formula logarithm the Frobenius morphism
2010/11/15
We show that the logarithm $\log_q$ of the Frobenius morphism $x\to x^q$ is given by the formula $x\to x\log x$ (the natural logarithm). In particular, it does not depend on $q$. This is the explicit ...
The convergence of the law of the logarithm involving negatively associated random fields
negatively associated random fields
2010/9/13
In this paper, the convergence of negatively associated random fields is investigated, two sufficiency conditions for the law of the logarithum are obtained by the Rosenthal and maximal Rosenthal ineq...
Precise rates in the law of iterated logarithm for the moment of I.I.D. random variables
the law of iterated logarithm strong approximation truncation method i.i.d. random variables
2007/12/12
Let $\{X, X_n; n\ge 1\}$ be a sequence of i.i.d. random variables, ${\rm E} X=0$, ${\rm E} X^2=\sigma^2<\infty$. Set $S_n=X_1+X_2+\cdots+X_n$, $M_n=\max_{k\le n}|S_k|$, $n\ge 1$. Let $a_n=O(1/\log\log...
A Berry-Esseen Theorem and a Law of the Iterated Logarithm for Asymptotically Negatively Associated Sequences
Berry--Esseen theorem law of the iterated logarithm negative association asymptotically negative association
2007/12/11
Negatively associated sequences have been studied extensively in recent years. Asymptotically negative association is a generalization of negative association. In this paper a Berry--Esseen theorem an...
On the Relationship between the Baum-Katz-Spitzer Complete Convergence Theorem and the Law of the Iterated Logarithm
partial sums of i.i.d. Banach space-valued random variables Baum--Katz--Spitzer complete convergence theorem law of the iterated logarithm almost sure convergence
2007/12/11
For a sequence of i.i.d. Banach space-valued random variables $\{X_{n}; ~n \geq 1 \}$ and a sequence of positive constants $\{a_{n}; ~n \geq 1 \}$, the relationship between the Baum--Katz--Spitzer com...