scholarly journals SOME FORMS FOR $ r^{th}$ MOVING MAXIMA OF ITERATED LOGARITHM LAW

2017 ◽  
Vol 30 (5) ◽  
Author(s):  
B. Almohaimeed
Keyword(s):  
Iterated Logarithm ◽  
Logarithm Law ◽  
Iterated Logarithm Law

scholarly journals On the central limit theorem and iterated logarithm law for stationary processes

1975 ◽  
Vol 12 (1) ◽  
pp. 1-8 ◽  
Author(s):  
C.C. Heyde
Keyword(s):  
Central Limit ◽  
Stationary Process ◽  
Stationary Processes ◽  
Martingale Differences ◽  
Stationary Increments ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
Logarithm Law ◽  
Functional Forms ◽  
Iterated Logarithm Law

It has recently emerged that a convenient way to establish central limit and iterated logarithm results for processes with stationary increments is to use approximating martingales with stationary increments. Functional forms of the limit results can be obtained via a representation for the increments of the stationary process in terms of stationary martingale differences plus other terms whose sum telescopes and disappears under suitable norming. Results based on the most general form of such a representation are here obtained.

A joint functional law for the Wiener process and principal value

2003 ◽  
Vol 40 (1-2) ◽  
pp. 213-241
Author(s):  
E. Csáki ◽  
A. Földes ◽  
Z. Shi
Keyword(s):  
Wiener Process ◽  
Local Times ◽  
Iterated Logarithm ◽  
Logarithm Law ◽  
Principal Value ◽  
Iterated Logarithm Law

We present a joint functional iterated logarithm law for the Wiener process and the principal value of its local times.

On the converse to the iterated logarithm law

1968 ◽  
Vol 5 (01) ◽  
pp. 210-215 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Random Variables ◽  
Iterated Logarithm ◽  
Logarithm Law ◽  
The Law ◽  
Image Position ◽  
Iterated Logarithm Law ◽  
Independent And Identically Distributed

Let Xi, i = 1, 2, 3,… be a sequence of independent and identically distributed random variables with law ℓ(X) and write. if EX = 0 and EX2 = σ2 < ∞, the law of the iterated logarithm (Hartman and Wintner [1]) tells us that

Some limit theorems for Markov branching processes

1973 ◽  
Vol 10 (02) ◽  
pp. 299-306 ◽  
Author(s):  
J. R. Leslie
Keyword(s):  
Limit Theorems ◽  
Branching Process ◽  
Branching Processes ◽  
Original Process ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
Logarithm Law ◽  
Increasing Process ◽  
Watson Process ◽  
Iterated Logarithm Law

Analogues of the central limit theorem and iterated logarithm law have recently been obtained for the Galton-Watson process; similar results are established in this paper for the temporally homogeneous Markov branching process and for the associated increasing process consisting of the number of splits in the original process up to time t.

An iterated logarithm result for martingales and its application in estimation theory for autoregressive processes

1973 ◽  
Vol 10 (1) ◽  
pp. 146-157 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Autoregressive Process ◽  
Rates Of Convergence ◽  
Estimation Theory ◽  
Autoregressive Processes ◽  
Sample Mean ◽  
Iterated Logarithm ◽  
Logarithm Law ◽  
Iterated Logarithm Law

The paper begins with an iterated logarithm law of classical Hartman-Wintner form for stationary martingales. This is then used to obtain iterated logarithm results giving information on rates of convergence of estimators of the parameters in a stationary autoregressive process. In the case of an autoregression of small order, detailed rate results for each autocorrelation and for the estimators of all parameters can be obtained. A rate result for the convergence of the sample mean is given in the general case.

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