On the Limiting Distribution of the Maximum Term in a Random Series

1992 ◽  
pp. 195-225 ◽  
Author(s):  
B. V. Gnedenko
Keyword(s):  
Limiting Distribution ◽  
Random Series ◽  
Maximum Term ◽  
Distribution Of The Maximum

The limiting distribution of the maximum term in a sequence of random variables defined on a markov chain

1970 ◽  
Vol 7 (3) ◽  
pp. 754-760 ◽  
Author(s):  
Augustus J. Fabens ◽  
Marcel F. Neuts
Keyword(s):  
Markov Chain ◽  
Random Variables ◽  
Limiting Distribution ◽  
Independent Random Variables ◽  
Finite Markov Chain ◽  
Maximum Term ◽  
Distribution Of The Maximum ◽  
Classical Work

SummaryGnedenko's classical work [1] on the limit of the distribution of the maximum of a sequence of independent random variables is extended to the distribution of the maximum of a sequence of random variables defined on a finite Markov chain.

The limiting distribution of the maximum term in a sequence of random variables defined on a markov chain

1970 ◽  
Vol 7 (03) ◽  
pp. 754-760 ◽  
Author(s):  
Augustus J. Fabens ◽  
Marcel F. Neuts
Keyword(s):  
Markov Chain ◽  
Random Variables ◽  
Limiting Distribution ◽  
Independent Random Variables ◽  
Finite Markov Chain ◽  
Maximum Term ◽  
Distribution Of The Maximum ◽  
Classical Work

Summary Gnedenko's classical work [1] on the limit of the distribution of the maximum of a sequence of independent random variables is extended to the distribution of the maximum of a sequence of random variables defined on a finite Markov chain.

The exponential rate of convergence of the distribution of the maximum of a random walk

1975 ◽  
Vol 12 (02) ◽  
pp. 279-288 ◽  
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Rate Of Convergence ◽  
Exponential Convergence ◽  
Random Variables ◽  
Limiting Distribution ◽  
Partial Sums ◽  
Exponential Rate ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence

Let Gn (x) be the distribution function of the maximum of the successive partial sums of independent and identically distributed random variables and G(x) its limiting distribution function. Under conditions, typical for complete exponential convergence, the decay of Gn (x) — G(x) is asymptotically equal to c.H(x)n −3/2 γn as n → ∞ where c and γ are known constants and H(x) is a function solely depending on x.

The exponential rate of convergence of the distribution of the maximum of a random walk

1975 ◽  
Vol 12 (2) ◽  
pp. 279-288 ◽  
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Rate Of Convergence ◽  
Exponential Convergence ◽  
Random Variables ◽  
Limiting Distribution ◽  
Partial Sums ◽  
Exponential Rate ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence

Let Gn(x) be the distribution function of the maximum of the successive partial sums of independent and identically distributed random variables and G(x) its limiting distribution function. Under conditions, typical for complete exponential convergence, the decay of Gn(x) — G(x) is asymptotically equal to c.H(x)n−3/2γn as n → ∞ where c and γ are known constants and H(x) is a function solely depending on x.

scholarly journals A Note on the Extremal Index for Space-Time Processes

2006 ◽  
Vol 43 (01) ◽  
pp. 114-126
Author(s):  
K. F. Turkman
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Domain Of Attraction ◽  
Extremal Index ◽  
Space Time ◽  
Limiting Distribution ◽  
Distribution Of The Maximum ◽  
Stationary Random Field

Let {X( s , t), s = (s 1, s 2) ∈ ℝ2, t ∈ ℝ} be a stationary random field defined over a discrete lattice. In this paper, we consider a set of domain of attraction criteria giving the notion of extremal index for random fields. Together with the extremal-types theorem given by Leadbetter and Rootzen (1997), this will give a characterization of the limiting distribution of the maximum of such random fields.

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