scholarly journals An elementary proof for dynamical scaling for certain fractional non-homogeneous Poisson processes

2021 ◽  
pp. 109296
Author(s):  
Markus Kreer
Keyword(s):  
Elementary Proof ◽  
Poisson Processes ◽  
Dynamical Scaling

An extension of watanabe's theorem of characterization of poisson processes over the positive real half line

1975 ◽  
Vol 12 (2) ◽  
pp. 396-399 ◽  
Author(s):  
P. Bremaud
Keyword(s):  
Poisson Process ◽  
Lebesgue Measure ◽  
Elementary Proof ◽  
Characterization Theorem ◽  
Poisson Processes ◽  
Half Line ◽  
Positive Real ◽  
The Mean ◽  
Martingale Characterization

We give an elementary proof of the martingale characterization theorem for Poisson processes over the positive real half line. This theorem is due to Watanabe [8] in the case where the mean measure associated to the Poisson process is the Lebesgue measure.

An extension of watanabe's theorem of characterization of poisson processes over the positive real half line

1975 ◽  
Vol 12 (02) ◽  
pp. 396-399 ◽  
Author(s):  
P. Bremaud
Keyword(s):  
Poisson Process ◽  
Lebesgue Measure ◽  
Elementary Proof ◽  
Characterization Theorem ◽  
Poisson Processes ◽  
Half Line ◽  
Positive Real ◽  
The Mean ◽  
Martingale Characterization

We give an elementary proof of the martingale characterization theorem for Poisson processes over the positive real half line. This theorem is due to Watanabe [8] in the case where the mean measure associated to the Poisson process is the Lebesgue measure.

AN ELEMENTARY PROOF OF A THEOREM OF LEE

1991 ◽  
Vol 11 (3) ◽  
pp. 356-360 ◽  
Author(s):  
Jia'an Yan
Keyword(s):  
Elementary Proof

scholarly journals A new elementary proof of a theorem of Minkowski

1926 ◽  
Vol 2 (3) ◽  
pp. 97-99
Author(s):  
Matsusaburô Fujiwara
Keyword(s):  
Elementary Proof

On some characterizations of the poisson process

1989 ◽  
Vol 26 (01) ◽  
pp. 176-181
Author(s):  
Wen-Jang Huang
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Arrival Time ◽  
Random Variables ◽  
Poisson Processes

In this article we give some characterizations of Poisson processes, the model which we consider is inspired by Kimeldorf and Thall (1983) and we generalize the results of Chandramohan and Liang (1985). More precisely, we consider an arbitrarily delayed renewal process, at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the ith new atom assigned to the process Di, i = 1, ···, k. We shall show that the existence of a pair of uncorrelated processes Di, Dj, i ≠ j, implies the renewal process is Poisson. Some other related characterization results are also obtained.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

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