scholarly journals Regenerative processes for Poisson zero polytopes

2018 ◽  
Vol 50 (4) ◽  
pp. 1217-1226
Author(s):  
Servet Martínez ◽  
Werner Nagel
Keyword(s):  
Markov Process ◽  
Important Application ◽  
Cell Process ◽  
Regenerative Processes ◽  
Stit Tessellation ◽  
Zero Cell ◽  
Bernoulli Flow

Abstract Let (Mt:t>0) be a Markov process of tessellations of ℝℓ, and let (𝒞t:t>0) be the process of their zero cells (zero polytopes), which has the same distribution as the corresponding process for Poisson hyperplane tessellations. In the present paper we describe the stationary zero cell process (at𝒞at:t∈ℝ),a>1, in terms of some regenerative structure and we show that it is a Bernoulli flow. An important application is to STIT tessellation processes.

On non-singular Markov renewal processes with an application to a growth–catastrophe model

1985 ◽  
Vol 22 (02) ◽  
pp. 253-266
Author(s):  
Seppo Niemi
Keyword(s):  
Markov Process ◽  
Total Variation ◽  
Population Model ◽  
Limit Theorems ◽  
Renewal Processes ◽  
Regenerative Processes ◽  
Catastrophe Model ◽  
Markov Renewal Processes ◽  
Harris Recurrence ◽  
Forward Process

The paper is concerned with Markov renewal processes satisfying a certain non-singularity condition. The relation of this condition to irreducibility, Harris recurrence and regularity of the associated forward Markov process is studied. This enables one to prove limit theorems of a total variation type for Markov renewal processes and semi-regenerative processes by applying Orey's theorem to the forward process. The results are applied to a GI/G/1 queue and a growth-catastrophe population model.

STIT tessellations are Bernoulli and standard

2012 ◽  
Vol 34 (3) ◽  
pp. 876-892 ◽  
Author(s):  
SERVET MARTÍNEZ
Keyword(s):  
Continuous Time ◽  
Bernoulli Shift ◽  
Random Sequence ◽  
Time Process ◽  
Continuous Time Process ◽  
Stit Tessellation ◽  
Bernoulli Flow

AbstractLet (Yt:t>0) be a STIT tessellation process and a>1. We prove that the random sequence (anYan:n∈ℤ) is a non-anticipating factor of a Bernoulli shift. We deduce that the continuous time process (atYat:t∈ℝ) is a Bernoulli flow. We use the techniques and results in Martínez and Nagel [Ergodic description of STIT tessellations. Stochastics 84(1) (2012), 113–134]. We also show that the filtration associated to the non-anticipating factor is standard in Vershik’s sense.

On non-singular Markov renewal processes with an application to a growth–catastrophe model

1985 ◽  
Vol 22 (2) ◽  
pp. 253-266 ◽  
Author(s):  
Seppo Niemi
Keyword(s):  
Markov Process ◽  
Total Variation ◽  
Population Model ◽  
Limit Theorems ◽  
Renewal Processes ◽  
Regenerative Processes ◽  
Catastrophe Model ◽  
Markov Renewal Processes ◽  
Harris Recurrence ◽  
Forward Process

The paper is concerned with Markov renewal processes satisfying a certain non-singularity condition. The relation of this condition to irreducibility, Harris recurrence and regularity of the associated forward Markov process is studied. This enables one to prove limit theorems of a total variation type for Markov renewal processes and semi-regenerative processes by applying Orey's theorem to the forward process. The results are applied to a GI/G/1 queue and a growth-catastrophe population model.

On effects of non-systematic reflections on weak-beam images of partial dislocations

1991 ◽  
Vol 49 ◽  
pp. 688-689
Author(s):  
K. Z. Botros ◽  
S. S. Sheinin
Keyword(s):  
High Precision ◽  
Stacking Fault ◽  
Important Application ◽  
Stacking Fault Energy ◽  
Sharp Peak ◽  
Weak Beam ◽  
Partial Dislocations ◽  
Deviation Parameter ◽  
Beam Diffraction

The main features of weak beam images of dislocations were first described by Cockayne et al. using calculations of intensity profiles based on the kinematical and two beam dynamical theories. The feature of weak beam images which is of particular interest in this investigation is that intensity profiles exhibit a sharp peak located at a position very close to the position of the dislocation in the crystal. This property of weak beam images of dislocations has an important application in the determination of stacking fault energy of crystals. This can easily be done since the separation of the partial dislocations bounding a stacking fault ribbon can be measured with high precision, assuming of course that the weak beam relationship between the positions of the image and the dislocation is valid. In order to carry out measurements such as these in practice the specimen must be tilted to "good" weak beam diffraction conditions, which implies utilizing high values of the deviation parameter Sg.

MANAGEMENT OF THE SUCCESS OF STUDENT’S LEARNING BASED ON THE MARKOV MODEL

2018 ◽  
pp. 4-11
Author(s):  
M. V. Noskov ◽  
M. V. Somova ◽  
I. M. Fedotova
Keyword(s):  
Information System ◽  
Markov Process ◽  
Continuous Time ◽  
Information Technologies ◽  
Educational Process ◽  
Automated Information System ◽  
The Subject ◽  
The University ◽  
Independent Work ◽  
Near Future

The article proposes a model for forecasting the success of student’s learning. The model is a Markov process with continuous time, such as the process of “death and reproduction”. As the parameters of the process, the intensities of the processes of obtaining and assimilating information are offered, and the intensity of the process of assimilating information takes into account the attitude of the student to the subject being studied. As a result of applying the model, it is possible for each student to determine the probability of a given formation of ownership of the material being studied in the near future. Thus, in the presence of an automated information system of the university, the implementation of the model is an element of the decision support system by all participants in the educational process. The examples given in the article are the results of an experiment conducted at the Institute of Space and Information Technologies of Siberian Federal University under conditions of blended learning, that is, under conditions when classroom work is accompanied by independent work with electronic resources.

Markov Process Model Forecasting of Quarterly Accounting Earnings Per Share

2011 ◽  
Vol 3 (6) ◽  
pp. 99-103
Author(s):  
M. P. Rajakumar M. P. Rajakumar ◽  
◽  
Dr. V. Shanthi Dr. V. Shanthi
Keyword(s):  
Markov Process ◽  
Process Model ◽  
Accounting Earnings ◽  
Earnings Per Share ◽  
Markov Process Model
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