Relative Volume as a Doubly Stochastic Binomial Point Process

2004 ◽  
Author(s):  
James McCulloch
Keyword(s):  
Point Process ◽  
Relative Volume ◽  
Doubly Stochastic ◽  
Binomial Point Process

Doubly stochastic Poisson point process driven by fractal shot noise

1991 ◽  
Vol 43 (8) ◽  
pp. 4192-4215 ◽  
Author(s):  
Steven B. Lowen ◽  
Malvin C. Teich
Keyword(s):  
Point Process ◽  
Shot Noise ◽  
Poisson Point Process ◽  
Doubly Stochastic

scholarly journals Poisson approximation for some point processes in reliability

2004 ◽  
Vol 36 (2) ◽  
pp. 455-470 ◽  
Author(s):  
Jean-Bernard Gravereaux ◽  
James Ledoux
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Poisson Approximation ◽  
Arrival Process ◽  
Homogeneous Poisson Process ◽  
Doubly Stochastic ◽  
Doubly Stochastic Poisson Process ◽  
Finite Markov Process ◽  
Failure Point

In this paper, we consider a failure point process related to the Markovian arrival process defined by Neuts. We show that it converges in distribution to a homogeneous Poisson process. This convergence takes place in the context of rare occurrences of failures. We also provide a convergence rate of the convergence in total variation of this point process using an approach developed by Kabanov, Liptser and Shiryaev for the doubly stochastic Poisson process driven by a finite Markov process.

scholarly journals Poisson approximation for some point processes in reliability

2004 ◽  
Vol 36 (02) ◽  
pp. 455-470
Author(s):  
Jean-Bernard Gravereaux ◽  
James Ledoux
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Poisson Approximation ◽  
Arrival Process ◽  
Homogeneous Poisson Process ◽  
Doubly Stochastic ◽  
Doubly Stochastic Poisson Process ◽  
Finite Markov Process ◽  
Failure Point

In this paper, we consider a failure point process related to the Markovian arrival process defined by Neuts. We show that it converges in distribution to a homogeneous Poisson process. This convergence takes place in the context of rare occurrences of failures. We also provide a convergence rate of the convergence in total variation of this point process using an approach developed by Kabanov, Liptser and Shiryaev for the doubly stochastic Poisson process driven by a finite Markov process.

scholarly journals BiPAD: Binomial Point Process Based Energy-Aware Data Dissemination in Opportunistic D2D Networks

Energies ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 2073
Author(s):  
Seho Han ◽  
Kisong Lee ◽  
Hyun-Ho Choi ◽  
Howon Lee
Keyword(s):  
Point Process ◽  
Routing Protocol ◽  
Data Dissemination ◽  
Optimal Number ◽  
Delivery Ratio ◽  
Message Delivery ◽  
Energy Aware ◽  
Epidemic Routing ◽  
Efficient Data ◽  
Binomial Point Process

In opportunistic device-to-device (D2D) networks, the epidemic routing protocol can be used to optimize the message delivery ratio. However, it has the disadvantage that it causes excessive coverage overlaps and wastes energy in message transmissions because devices are more likely to receive duplicates from neighbors. We therefore propose an efficient data dissemination algorithm that can reduce undesired transmission overlap with little performance degradation in the message delivery ratio. The proposed algorithm allows devices further away than the k-th furthest distance from the source device to forward a message to their neighbors. These relay devices are determined by analysis based on a binomial point process (BPP). Using a set of intensive simulations, we present the resulting network performances with respect to the total number of received messages, the forwarding efficiency and the actual number of relays. In particular, we find the optimal number of relays to achieve almost the same message delivery ratio as the epidemic routing protocol for a given network deployment. Furthermore, the proposed algorithm can achieve almost the same message delivery ratio as the epidemic routing protocol while improving the forwarding efficiency by over 103% when k≥10.

Point processes generated by transitions of Markov chains

1973 ◽  
Vol 5 (2) ◽  
pp. 262-286 ◽  
Author(s):  
Mats Rudemo
Keyword(s):  
Markov Chain ◽  
Point Process ◽  
Point Processes ◽  
Queueing System ◽  
Initial Distribution ◽  
Recurrence Time ◽  
Asynchronous Sampling ◽  
Doubly Stochastic ◽  
Special Cases ◽  
Forward Recurrence Time

For a continuous time Markov chain the time points of transitions, belonging to a subset of the set of all transitions, are observed. Special cases include the point process generated by all transitions and doubly stochastic Poisson processes with a Markovian intensity. Equations are derived for the conditional distribution of the state of the Markov chain, given observations of the point process. This distribution may be used for prediction. For the forward recurrence time of the point process, distributions corresponding to synchronous and asynchronous sampling are also derived. The Palm distribution for the point process is specified in terms of the corresponding initial distribution for the Markov chain. In examples the point processes of arrivals and departures in a queueing system are studied. Two biological applications deal with estimation of population size and detection of epidemics.

Doubly stochastic Poisson processes and process control

1972 ◽  
Vol 4 (02) ◽  
pp. 318-338 ◽  
Author(s):  
Mats Rudemo
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
State Space ◽  
Point Process ◽  
Doubly Stochastic ◽  
Long Run ◽  
Finite State ◽  
Control State ◽  
Special Case ◽  
Finite State Space

Consider a Poisson point process with an intensity parameter forming a Markov chain with continuous time and finite state space. A system of ordinary differential equations is derived for the conditional distribution of the Markov chain given observations of the point process. An estimate of the current intensity, optimal in the least-squares sense, is computed from this distribution. Applications to reliability and replacement theory are given. A special case with two states, corresponding to a process in control and out of control, is discussed at length. Adjustment rules, based on the conditional probability of the out of control state, are studied. Regarded as a function of time, this probability forms a Markov process with the unit interval as state space. For the distribution of this process, integro-differential equations are derived. They are used to compute the average long run cost of adjustment rules.

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