Limiting behaviour of the sum of I.I.D. random variables and its terms of greatest moduli in the case of logarithmic type tall function

1989 ◽  
pp. 22-32 ◽  
Author(s):  
I. Factorovich
Keyword(s):  
Random Variables ◽  
Limiting Behaviour ◽  
Logarithmic Type

Integer-valued branching processes with immigration

1983 ◽  
Vol 15 (04) ◽  
pp. 713-725 ◽  
Author(s):  
F. W. Steutel ◽  
W. Vervaat ◽  
S. J. Wolfe
Keyword(s):  
Difference Equation ◽  
Continuous Time ◽  
Queueing Theory ◽  
Branching Processes ◽  
Random Variables ◽  
Discrete State ◽  
Limiting Behaviour ◽  
Supercritical Branching Processes

The notion of self-decomposability for -valued random variables as introduced by Steutel and van Harn [10] and its generalization by van Harn, Steutel and Vervaat [5], are used to study the limiting behaviour of continuous-time Markov branching processes with immigration. This behaviour provides analogues to the behaviour of sequences of random variables obeying a certain difference equation as studied by Vervaat [12] and their continuous-time counterpart considered by Wolfe [13]. An application in queueing theory is indicated. Furthermore, discrete-state analogues are given for results on stability in the processes studied by Wolfe, and for results on self-decomposability in supercritical branching processes by Yamazato [14].

Integer-valued branching processes with immigration

1983 ◽  
Vol 15 (4) ◽  
pp. 713-725 ◽  
Author(s):  
F. W. Steutel ◽  
W. Vervaat ◽  
S. J. Wolfe
Keyword(s):  
Difference Equation ◽  
Continuous Time ◽  
Queueing Theory ◽  
Branching Processes ◽  
Random Variables ◽  
Discrete State ◽  
Limiting Behaviour ◽  
Supercritical Branching Processes

The notion of self-decomposability for -valued random variables as introduced by Steutel and van Harn [10] and its generalization by van Harn, Steutel and Vervaat [5], are used to study the limiting behaviour of continuous-time Markov branching processes with immigration. This behaviour provides analogues to the behaviour of sequences of random variables obeying a certain difference equation as studied by Vervaat [12] and their continuous-time counterpart considered by Wolfe [13]. An application in queueing theory is indicated. Furthermore, discrete-state analogues are given for results on stability in the processes studied by Wolfe, and for results on self-decomposability in supercritical branching processes by Yamazato [14].

The extremal index and clustering of high values for derived stationary sequences

1995 ◽  
Vol 32 (4) ◽  
pp. 972-981 ◽  
Author(s):  
Ishay Weissman ◽  
Uri Cohen
Keyword(s):  
Random Variables ◽  
Extremal Index ◽  
Stationary Sequence ◽  
Stationary Sequences ◽  
Limiting Behaviour ◽  
Maximum Sequence ◽  
Independent Identically Distributed ◽  
Pointwise Maximum

Given a sequence of independent identically distributed random variables, we derive a moving-maximum sequence (with random translations). The extremal index of the derived sequence is computed and the limiting behaviour of clusters of high values is studied. We are then given two or more independent stationary sequences whose extremal indices are known. We derive a new stationary sequence by taking either a pointwise maximum or by a mixture of the original sequences. In each case, we compute the extremal index of the derived sequence.

The limiting behaviour of the maximal spacing generated by an i.i.d. sequence of Gaussian random variables

1985 ◽  
Vol 22 (04) ◽  
pp. 816-827
Author(s):  
Paul Deheuvels
Keyword(s):  
Random Variables ◽  
Limiting Distribution ◽  
Gaussian Random Variables ◽  
Limiting Behaviour ◽  
Independent And Identically Distributed

LetMnbe the maximal spacing generated in the sample's range byΧ1,· ··,Χn, independent and identically distributed Gaussian N(0, 1) random variables. We obtain the limiting distribution ofand show thataccording to whether ε> 0 orε< 0.

Limiting behaviour for arrays of rowwise widely orthant dependent random variables under conditions of R − h-integrability and its applications

Stochastics ◽  
2019 ◽  
Vol 91 (6) ◽  
pp. 916-944 ◽  
Author(s):  
Yi Wu ◽  
Xuejun Wang ◽  
Tien-Chung Hu ◽  
Manuel Ordonez Cabrera ◽  
Andrei Volodin
Keyword(s):  
Random Variables ◽  
Dependent Random Variables ◽  
Limiting Behaviour ◽  
Widely Orthant Dependent

scholarly journals Limits of compound and thinned point processes

1975 ◽  
Vol 12 (2) ◽  
pp. 269-278 ◽  
Author(s):  
Olav Kallenberg
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Random Variables ◽  
Random Measure ◽  
Poisson Processes ◽  
Limiting Behaviour ◽  
Mutually Independent

Let η =Σjδτj be a point process on some space S and let β,β1,β2, … be identically distributed non-negative random variables which are mutually independent and independent of η. We can then form the compound point process ξ = Σjβjδτj which is a random measure on S. The purpose of this paper is to study the limiting behaviour of ξ as . In the particular case when β takes the values 1 and 0 with probabilities p and 1 –p respectively, ξ becomes a p-thinning of η and our theorems contain some classical results by Rényi and others on the thinnings of a fixed process, as well as a characterization by Mecke of the class of subordinated Poisson processes.

Convergence in distribution of lightly trimmed and untrimmed sums are equivalent

1993 ◽  
Vol 113 (3) ◽  
pp. 615-638 ◽  
Author(s):  
Harry Kesten
Keyword(s):  
Limit Distribution ◽  
Random Variables ◽  
Fixed Number ◽  
Convergence In Distribution ◽  
Trimmed Sums ◽  
Limiting Behaviour ◽  
Modest Effect

AbstractWe show that trimming a fixed number of terms from sums of i.i.d. random variables (so-called light trimming) can have only a modest effect on limiting behaviour. More specifically, the trimmed sums, after centralization and normalization, have a limit distribution, if and only if the untrimmed sums have a limit distribution (with the same centralization and normalization constants).

The extremal index and clustering of high values for derived stationary sequences

1995 ◽  
Vol 32 (04) ◽  
pp. 972-981 ◽  
Author(s):  
Ishay Weissman ◽  
Uri Cohen
Keyword(s):  
Random Variables ◽  
Extremal Index ◽  
Stationary Sequence ◽  
Stationary Sequences ◽  
Limiting Behaviour ◽  
Maximum Sequence ◽  
Independent Identically Distributed ◽  
Pointwise Maximum

Given a sequence of independent identically distributed random variables, we derive a moving-maximum sequence (with random translations). The extremal index of the derived sequence is computed and the limiting behaviour of clusters of high values is studied. We are then given two or more independent stationary sequences whose extremal indices are known. We derive a new stationary sequence by taking either a pointwise maximum or by a mixture of the original sequences. In each case, we compute the extremal index of the derived sequence.

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