scholarly journals Kekonvergenan MSE Penduga Kernel Seragam Fungsi Intensitas Proses Poisson Periodik dengan Tren Fungsi Pangkat

2012 ◽  
Vol 3 (1) ◽  
pp. 204
Author(s):  
Ro’fah Nur Rachmawati
Keyword(s):  
Stochastic Process ◽  
Poisson Process ◽  
Continuous Time ◽  
Kernel Estimator ◽  
Intensity Function ◽  
Rank Function ◽  
Service Center ◽  
Discrete State ◽  
Number Of Customers ◽  
Discrete State Space

The number of customers who come to a service center will be different for each particular time. However, it can be modeled by a stochastic process. One particular form of stochastic process with continuous time and discrete state space is a periodic Poisson process. The intensity function of the process is generally unknown, so we need a method to estimate it. In this paper an estimator of kernel uniform of a periodic Poisson process is formulated with a trend component in a rank function (rank coefficient 0 <b <1 is known, and the slope coefficient of the power function (trend) a> 0 is known). It is also demonstrated the convergenity of the estimators obtained. The result of this paper is a formulation of a uniform kernel estimator for the intensity function of a periodic Poisson process with rank function trends (for the case “a” is known) and the convergenity proof of the estimators obtained.

scholarly journals Pendugaan Fungsi Intensitas Proses Poisson Periodik dengan Tren Fungsi Pangkat Menggunakan Metode Tipe Kernel

2011 ◽  
Vol 2 (1) ◽  
pp. 458
Author(s):  
Ro’fah Nur Rachmawati
Keyword(s):  
Stochastic Process ◽  
Poisson Process ◽  
Customer Service ◽  
Kernel Estimator ◽  
Intensity Function ◽  
Rank Function ◽  
Discrete State ◽  
Function Coefficient ◽  
Number Of Customers ◽  
Discrete State Space

Stochastic process has an important role in many areas in everyday life, including the customer service process. The number of customers who come to a service center will be different for each particular time. A special form of stochastic process with continuous time and discrete state space is periodic Poisson process, which is a Poisson process with an intensity function of a periodic function. However, on the stochastic modeling of a phenomenon by a periodic Poisson process, the intensity function of the process is generally unknown. Therefore, a method is needed to infer the function. In this article, a Kernel estimator is formulated from a periodic Poisson process with a trend component in a rank function, which is divided into two cases; the identified rank function coefficient and the unidentified rank function coefficient. 

Asymptotic behaviour of continuous time, continuous state-space branching processes

1974 ◽  
Vol 11 (04) ◽  
pp. 669-677 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Asymptotic Behaviour ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Discrete State ◽  
Space And Time ◽  
Continuous State Space ◽  
Continuous State ◽  
Discrete State Space

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.

Randomization of intensities in a Markov chain

1979 ◽  
Vol 11 (2) ◽  
pp. 397-421 ◽  
Author(s):  
M. Yadin ◽  
R. Syski
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
State Space ◽  
Continuous Time ◽  
Markovian Process ◽  
Time Parameter ◽  
Discrete State ◽  
Intensity Matrix ◽  
The Matrix ◽  
Discrete State Space

The matrix of intensities of a Markov process with discrete state space and continuous time parameter undergoes random changes in time in such a way that it stays constant between random instants. The resulting non-Markovian process is analyzed with the help of supplementary process defined in terms of variations of the intensity matrix. Several examples are presented.

scholarly journals Using model-based proposals for fast parameter inference on discrete state space, continuous-time Markov processes

2015 ◽  
Vol 12 (107) ◽  
pp. 20150225 ◽  
Author(s):  
C. M. Pooley ◽  
S. C. Bishop ◽  
G. Marion
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Continuous Time ◽  
Dynamic Models ◽  
Model Systems ◽  
Model Parameters ◽  
Discrete State ◽  
State Variable ◽  
Model Based ◽  
Discrete State Space

Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob–Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed ‘model-based proposal’ (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2–8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large.

Asymptotic behaviour of continuous time, continuous state-space branching processes

1974 ◽  
Vol 11 (4) ◽  
pp. 669-677 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Asymptotic Behaviour ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Discrete State ◽  
Space And Time ◽  
Continuous State Space ◽  
Continuous State ◽  
Discrete State Space

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.

Randomization of intensities in a Markov chain

1979 ◽  
Vol 11 (02) ◽  
pp. 397-421
Author(s):  
M. Yadin ◽  
R. Syski
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
State Space ◽  
Continuous Time ◽  
Markovian Process ◽  
Time Parameter ◽  
Discrete State ◽  
Intensity Matrix ◽  
The Matrix ◽  
Discrete State Space

The matrix of intensities of a Markov process with discrete state space and continuous time parameter undergoes random changes in time in such a way that it stays constant between random instants. The resulting non-Markovian process is analyzed with the help of supplementary process defined in terms of variations of the intensity matrix. Several examples are presented.

On an optimal selection problem of Cowan and Zabczyk

1987 ◽  
Vol 24 (4) ◽  
pp. 918-928 ◽  
Author(s):  
F. Thomas Bruss
Keyword(s):  
Poisson Process ◽  
Continuous Time ◽  
Intensity Function ◽  
Poisson Processes ◽  
Secretary Problem ◽  
Selection Problem ◽  
Recall Condition ◽  
Optimal Selection ◽  
Multiplicative Constant ◽  
Inhomogeneous Poisson Process

Cowan and Zabczyk (1978) have studied a continuous-time generalization of the so-called secretary problem, where options arise according to a homogeneous Poisson processes of known intensity λ. They gave the complete strategy maximizing the probability of accepting the best option under the usual no-recall condition. In this paper, the solution is extended to the case where the intensity λ is unknown, and also to the case of an inhomogeneous Poisson process with intensity function λ (t), which is either supposed to be known or known up to a multiplicative constant.

scholarly journals Randomised rules for stopping problems

2020 ◽  
Vol 57 (3) ◽  
pp. 981-1004
Author(s):  
David Hobson ◽  
Matthew Zeng
Keyword(s):  
Stochastic Process ◽  
Poisson Process ◽  
Optimal Stopping ◽  
Continuous Time ◽  
Optimal Stopping Problem ◽  
Time Optimal ◽  
Time Formulation ◽  
Event Times ◽  
Limiting Case ◽  
Independent Poisson Process

AbstractIn a classical, continuous-time, optimal stopping problem, the agent chooses the best time to stop a stochastic process in order to maximise the expected discounted return. The agent can choose when to stop, and if at any moment they decide to stop, stopping occurs immediately with probability one. However, in many settings this is an idealistic oversimplification. Following Strack and Viefers we consider a modification of the problem in which stopping occurs at a rate which depends on the relative values of stopping and continuing: there are several different solutions depending on how the value of continuing is calculated. Initially we consider the case where stopping opportunities are constrained to be event times of an independent Poisson process. Motivated by the limiting case as the rate of the Poisson process increases to infinity, we also propose a continuous-time formulation of the problem where stopping can occur at any instant.

On an optimal selection problem of Cowan and Zabczyk

1987 ◽  
Vol 24 (04) ◽  
pp. 918-928 ◽  
Author(s):  
F. Thomas Bruss
Keyword(s):  
Poisson Process ◽  
Continuous Time ◽  
Intensity Function ◽  
Poisson Processes ◽  
Secretary Problem ◽  
Selection Problem ◽  
Recall Condition ◽  
Optimal Selection ◽  
Multiplicative Constant ◽  
Inhomogeneous Poisson Process

Cowan and Zabczyk (1978) have studied a continuous-time generalization of the so-called secretary problem, where options arise according to a homogeneous Poisson processes of known intensity λ. They gave the complete strategy maximizing the probability of accepting the best option under the usual no-recall condition. In this paper, the solution is extended to the case where the intensity λ is unknown, and also to the case of an inhomogeneous Poisson process with intensity function λ (t), which is either supposed to be known or known up to a multiplicative constant.

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