scholarly journals Long runs under a conditional limit distribution

2014 ◽  
Vol 24 (6) ◽  
pp. 2246-2296 ◽  
Author(s):  
Michel Broniatowski ◽  
Virgile Caron
Keyword(s):  
Limit Distribution ◽  
Conditional Limit

On the quasi-stationary distributions of the GI/M/1 queue

1972 ◽  
Vol 9 (01) ◽  
pp. 117-128 ◽  
Author(s):  
E. K. Kyprianou
Keyword(s):  
Gamma Distribution ◽  
Waiting Time ◽  
Limit Distribution ◽  
Weighted Sum ◽  
Traffic Intensity ◽  
Time Process ◽  
Queue Size ◽  
Virtual Waiting Time ◽  
Waiting Time Process ◽  
Conditional Limit

This paper studies the existence, in a stable GI/M/1 queue, of the limit as t → ∞ of the distribution of the virtual waiting time process at time t conditioned on the event that at no time in the interval [0, t] the queue has become empty. The conditional limit distribution obtained when the traffic intensity is strictly less than one is the weighted sum of an exponential and a gamma distribution. Similar conditional limit distributions are obtained for the queue size process and the waiting time process as defined by Prabhu (1964).

On the quasi-stationary distributions of the GI/M/1 queue

1972 ◽  
Vol 9 (1) ◽  
pp. 117-128 ◽  
Author(s):  
E. K. Kyprianou
Keyword(s):  
Gamma Distribution ◽  
Waiting Time ◽  
Limit Distribution ◽  
Weighted Sum ◽  
Traffic Intensity ◽  
Time Process ◽  
Queue Size ◽  
Virtual Waiting Time ◽  
Waiting Time Process ◽  
Conditional Limit

This paper studies the existence, in a stable GI/M/1 queue, of the limit as t → ∞ of the distribution of the virtual waiting time process at time t conditioned on the event that at no time in the interval [0, t] the queue has become empty. The conditional limit distribution obtained when the traffic intensity is strictly less than one is the weighted sum of an exponential and a gamma distribution. Similar conditional limit distributions are obtained for the queue size process and the waiting time process as defined by Prabhu (1964).

Efficiency, Sufficiency, and Optimality

2017 ◽  
Author(s):  
Amos Golan
Keyword(s):  
Limit Theorem ◽  
Computational Efficiency ◽  
The Other ◽  
Information Compression ◽  
Information Theoretic ◽  
Conditional Limit Theorem ◽  
Concept Of Information ◽  
Conditional Limit

In this chapter I provide additional rationalization for using the info-metrics framework. This time the justifications are in terms of the statistical, mathematical, and information-theoretic properties of the formalism. Specifically, in this chapter I discuss optimality, statistical and computational efficiency, sufficiency, the concentration theorem, the conditional limit theorem, and the concept of information compression. These properties, together with the other properties and measures developed in earlier chapters, provide logical, mathematical, and statistical justifications for employing the info-metrics framework.

On the first zero of an empirical characteristic function

1991 ◽  
Vol 28 (3) ◽  
pp. 593-601 ◽  
Author(s):  
H. U. Bräker ◽  
J. Hüsler
Keyword(s):  
Characteristic Function ◽  
Limit Distribution ◽  
Random Variable ◽  
Empirical Characteristic Function ◽  
The Real ◽  
Exponential Decrease ◽  
Characteristic Process

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

scholarly journals Non-local Solvable Birth–Death Processes

2021 ◽  
Author(s):  
Giacomo Ascione ◽  
Nikolai Leonenko ◽  
Enrica Pirozzi
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Limit Distribution ◽  
Spectral Decomposition ◽  
Strong Solutions ◽  
Stochastic Representation ◽  
Discrete Approximations ◽  
Local Difference ◽  
Non Local ◽  
Birth Death

AbstractIn this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.

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