Asymptotic enlarging of semi-markov processes with an arbitrary state space

1976 ◽  
pp. 297-315 ◽  
Author(s):  
V. S. Korolyuk ◽  
A. F. Turbin
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Arbitrary State ◽  
Semi Markov Processes

Stochastic Petri Nets: Modeling Power and Limit Theorems

1991 ◽  
Vol 5 (4) ◽  
pp. 477-498 ◽  
Author(s):  
Peter J. Haas ◽  
Gerald S. Shedler
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Markov Processes ◽  
Discrete Event ◽  
Building Blocks ◽  
The State ◽  
Stochastic Petri Nets ◽  
Transition Mechanism ◽  
Modeling Power ◽  
Semi Markov Processes

Generalized semi-Markov processes and stochastic Petri nets provide building blocks for specification of discrete event system simulations on a finite or countable state space. The two formal systems differ, however, in the event scheduling (clock-setting) mechanism, the state transition mechanism, and the form of the state space. We have shown previously that stochastic Petri nets have at least the modeling power of generalized semi-Markov processes. In this paper we show that stochastic Petri nets and generalized semi-Markov processes, in fact, have the same modeling power. Combining this result with known results for generalized semi-Markov processes, we also obtain conditions for time-average convergence and convergence in distribution along with a central limit theorem for the marking process of a stochastic Petri net.

Quasi-stationary distributions in semi-Markov processes

1970 ◽  
Vol 7 (02) ◽  
pp. 388-399 ◽  
Author(s):  
C. K. Cheong
Keyword(s):  
Markov Process ◽  
State Space ◽  
Markov Processes ◽  
Transition Probability ◽  
Main Concern ◽  
Initial State ◽  
Stationary Distributions ◽  
Semi Markov Process ◽  
Image Position ◽  
Semi Markov Processes

Our main concern in this paper is the convergence, as t → ∞, of the quantities i, j ∈ E; where Pij (t) is the transition probability of a semi-Markov process whose state space E is irreducible but not closed (i.e., escape from E is possible), and rj is the probability of eventual escape from E conditional on the initial state being i. The theorems proved here generalize some results of Seneta and Vere-Jones ([8] and [11]) for Markov processes.

A SUCCESSIVE LUMPING PROCEDURE FOR A CLASS OF MARKOV CHAINS

2012 ◽  
Vol 26 (4) ◽  
pp. 483-508 ◽  
Author(s):  
Michael N. Katehakis ◽  
Laurens C. Smit
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Queueing Models ◽  
Semi Markov Processes ◽  
Stationary Probabilities

A class of Markov chains we call successively lumbaple is specified for which it is shown that the stationary probabilities can be obtained by successively computing the stationary probabilities of a propitiously constructed sequence of Markov chains. Each of the latter chains has a(typically much) smaller state space and this yields significant computational improvements. We discuss how the results for discrete time Markov chains extend to semi-Markov processes and continuous time Markov processes. Finally, we will study applications of successively lumbaple Markov chains to classical reliability and queueing models.

Quasi-stationary distributions in semi-Markov processes

1970 ◽  
Vol 7 (2) ◽  
pp. 388-399 ◽  
Author(s):  
C. K. Cheong
Keyword(s):  
Markov Process ◽  
State Space ◽  
Markov Processes ◽  
Transition Probability ◽  
Main Concern ◽  
Initial State ◽  
Stationary Distributions ◽  
Semi Markov Process ◽  
Image Position ◽  
Semi Markov Processes

Our main concern in this paper is the convergence, as t → ∞, of the quantities i, j ∈ E; where Pij(t) is the transition probability of a semi-Markov process whose state space E is irreducible but not closed (i.e., escape from E is possible), and rj is the probability of eventual escape from E conditional on the initial state being i. The theorems proved here generalize some results of Seneta and Vere-Jones ([8] and [11]) for Markov processes.

scholarly journals On application of semi-Markov processes superposition to energy systems modeling

2019 ◽  
Vol 139 ◽  
pp. 01064
Author(s):  
Yuriy E. Obzherin ◽  
Stanislav M. Sidorov ◽  
Mikhail M. Nikitin
Keyword(s):  
Information Systems ◽  
Mathematical Models ◽  
State Space ◽  
Markov Processes ◽  
Phase State ◽  
Energy Systems ◽  
Systems Modeling ◽  
Intelligent Management ◽  
Semi Markov Processes

One of the important tasks of the theory of reliability and efficiency of energy systems is the task of creating information systems for managing energy systems and the transition to intelligent management and engineering. The solution to this problem is possible based on the construction of mathematical models relating to various aspects of the structure and functioning of these systems. The paper, using the example of a superposition of independent semi-Markov processes constructed in the works of V.S. Korolyuk, A.F. Turbin, examines the possibilities of using semi-Markov processes with a common phase state space for modeling energy systems; an illustrative example of the application of this approach is given.

Semi-Markov processes on a general state space: α-theory and quasi-stationarity

1980 ◽  
Vol 30 (2) ◽  
pp. 187-200 ◽  
Author(s):  
E. Arjas ◽  
E. Nummelin ◽  
R. L. Tweedie
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Limit Theorems ◽  
General State ◽  
General State Space ◽  
Quasistationary Distributions ◽  
Positive Recurrent ◽  
Semi Markov Processes

AbstractBy amalgamating the approaches of Tweedie (1974) and Nummelin (1977), an α-theory is developed for general semi-Markov processes. It is shown that α-transient, α-recurrent and α-positive recurrent processes can be defined, with properties analogous to those for transient, recurrent and positive recurrent processes. Limit theorems for α-positive recurrent processes follow by transforming to the probabilistic case, as in the above references: these then give results on the existence and form of quasistationary distributions, extending those of Tweedie (1975) and Nummelin (1976).

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