scholarly journals Acknowledgment of Priority: Asymptotic Theory of a Test for the Constancy of Regression Coefficients Against the Random Walk Alternative

1994 ◽  
Vol 22 (1) ◽  
pp. 563-563 ◽  
Author(s):  
Seiji Nabeya ◽  
Katsuto Tanaka
Keyword(s):  
Random Walk ◽  
Asymptotic Theory ◽  
Regression Coefficients ◽  
Constancy Of Regression

On Testing for the Constancy of Regression Coefficients under Random Walk and Change-Point Alternatives

1992 ◽  
Vol 8 (4) ◽  
pp. 501-517 ◽  
Author(s):  
V.K. Jandhyala ◽  
I.B. MacNeill
Keyword(s):  
Random Walk ◽  
Change Point ◽  
Asymptotic Theory ◽  
Regression Coefficients ◽  
Type Statistic ◽  
Invariant Statistic ◽  
Constancy Of Regression

The locally best invariant statistic to test for the constancy of regression coefficients under a random walk alternative is shown to be the same as a Bayesian-type statistic derived under a change-point alternative. Asymptotic theory for this and more general statistics is discussed.

scholarly journals Gumbel and Fréchet convergence of the maxima of independent random walks

2020 ◽  
Vol 52 (1) ◽  
pp. 213-236 ◽  
Author(s):  
Thomas Mikosch ◽  
Jorge Yslas
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Point Process ◽  
Asymptotic Theory ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Independent Random Variables ◽  
Finite Moment ◽  
Process Convergence ◽  
Precise Large Deviation

AbstractWe consider point process convergence for sequences of independent and identically distributed random walks. The objective is to derive asymptotic theory for the largest extremes of these random walks. We show convergence of the maximum random walk to the Gumbel or the Fréchet distributions. The proofs depend heavily on precise large deviation results for sums of independent random variables with a finite moment generating function or with a subexponential distribution.

Branching random walk in varying environments

1982 ◽  
Vol 14 (02) ◽  
pp. 359-367 ◽  
Author(s):  
C. F. Klebaner
Keyword(s):  
Random Walk ◽  
Asymptotic Theory ◽  
Sufficient Conditions ◽  
Almost Sure Convergence ◽  
Point Of View ◽  
Branching Random Walk ◽  
Time Interval ◽  
The Central Limit Theorem ◽  
Age Dependent ◽  
Varying Environments

The branching random walk model is generalized towards generation-dependent displacement and reproduction distributions. Asymptotic theory of branching random walk in varying environments from theL2point of view is given. IfZn(x) is the number of nth-generation particles to the left ofx, then under appropriate conditions for suitably chosenxn,Zn(xn)/Zn(+∞) converges inL2completely to a limiting distribution. Sufficient conditions for almost sure convergence are given. As a corollary an analogue of the central limit theorem for the proportion of particles of the nth generation in time intervalInin the age-dependent Crump–Mode–Jagers process is obtained.

Branching random walk in varying environments

1982 ◽  
Vol 14 (2) ◽  
pp. 359-367 ◽  
Author(s):  
C. F. Klebaner
Keyword(s):  
Random Walk ◽  
Asymptotic Theory ◽  
Sufficient Conditions ◽  
Almost Sure Convergence ◽  
Point Of View ◽  
Branching Random Walk ◽  
Time Interval ◽  
The Central Limit Theorem ◽  
Age Dependent ◽  
Varying Environments

The branching random walk model is generalized towards generation-dependent displacement and reproduction distributions. Asymptotic theory of branching random walk in varying environments from the L2 point of view is given. If Zn(x) is the number of nth-generation particles to the left of x, then under appropriate conditions for suitably chosen xn, Zn (xn)/Zn (+∞) converges in L2 completely to a limiting distribution. Sufficient conditions for almost sure convergence are given. As a corollary an analogue of the central limit theorem for the proportion of particles of the nth generation in time interval In in the age-dependent Crump–Mode–Jagers process is obtained.

Elements of the Random Walk

2004 ◽  
Author(s):  
Joseph Rudnick ◽  
George Gaspari
Keyword(s):  
Random Walk
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