On Levy's theorem concerning positiveness of transition probabilities of Markov processes: the circuit processes case

1993 ◽  
Vol 30 (1) ◽  
pp. 28-39 ◽  
Author(s):  
S. Kalpazidou
Keyword(s):  
Probability Distribution ◽  
State Space ◽  
Markov Processes ◽  
Transition Probabilities ◽  
The State ◽  
Sample Paths ◽  
Lévy’S Theorem

We prove Lévy's theorem concerning positiveness of transition probabilities of Markov processes when the state space is countable and an invariant probability distribution exists. Our approach relies on the representation of transition probabilities in terms of the directed circuits that occur along the sample paths.

On Levy's theorem concerning positiveness of transition probabilities of Markov processes: the circuit processes case

1993 ◽  
Vol 30 (01) ◽  
pp. 28-39
Author(s):  
S. Kalpazidou
Keyword(s):  
Probability Distribution ◽  
State Space ◽  
Markov Processes ◽  
Transition Probabilities ◽  
The State ◽  
Sample Paths ◽  
Lévy’S Theorem

We prove Lévy's theorem concerning positiveness of transition probabilities of Markov processes when the state space is countable and an invariant probability distribution exists. Our approach relies on the representation of transition probabilities in terms of the directed circuits that occur along the sample paths.

Kolmogorov's differential equations for non-stationary, countable state Markov processes with uniformly continuous transition probabilities

1973 ◽  
Vol 73 (1) ◽  
pp. 119-138 ◽  
Author(s):  
Gerald S. Goodman ◽  
S. Johansen
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
State Space ◽  
Markov Processes ◽  
Transition Probabilities ◽  
The State ◽  
Continuous Transition ◽  
Countable State Space ◽  
Countable State ◽  
Uniformly Continuous

1. SummaryWe shall consider a non-stationary Markov chain on a countable state space E. The transition probabilities {P(s, t), 0 ≤ s ≤ t <t0 ≤ ∞} are assumed to be continuous in (s, t) uniformly in the state i ε E.

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.

Some results about Markov processes on subsets of the state space

1976 ◽  
Vol 8 (3) ◽  
pp. 517-530 ◽  
Author(s):  
Cristina Gzyl
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Joint Distribution ◽  
Regular Point ◽  
The State ◽  
Hunt Process ◽  
Perfect Subset ◽  
Image Position

Kingman [5] proved a formula that expresses the joint distribution of the processes where b is a regular point in the state space of a Hunt process. We give an extension of this formula, as well as several interesting facts related to it, for the case when Φ is any finely perfect subset of the state space. We also establish some connections between this result and results on last-exit decompositions.

Some results about Markov processes on subsets of the state space

1976 ◽  
Vol 8 (03) ◽  
pp. 517-530 ◽  
Author(s):  
Cristina Gzyl
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Joint Distribution ◽  
Regular Point ◽  
The State ◽  
Hunt Process ◽  
Perfect Subset ◽  
Image Position

Kingman [5] proved a formula that expresses the joint distribution of the processes where b is a regular point in the state space of a Hunt process. We give an extension of this formula, as well as several interesting facts related to it, for the case when Φ is any finely perfect subset of the state space. We also establish some connections between this result and results on last-exit decompositions.

scholarly journals First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Mario Lefebvre ◽  
Jean-Luc Guilbault
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Transition Probabilities ◽  
The State ◽  
Discrete Version ◽  
Uhlenbeck Process ◽  
Current State ◽  
Ornstein Uhlenbeck Process

A Markov chain with state space{0,…,N}and transition probabilities depending on the current state is studied. The chain can be considered as a discrete Ornstein-Uhlenbeck process. The probability that the process hitsNbefore 0 is computed explicitly. Similarly, the probability that the process hitsNbefore−Mis computed in the case when the state space is{−M,…,0,…,N}and the transition probabilitiespi,i+1are not necessarily the same wheniis positive andiis negative.

Ergodic decompositions associated with regular Markov operators on Polish spaces

2010 ◽  
Vol 31 (2) ◽  
pp. 571-597 ◽  
Author(s):  
DANIËL T. H. WORM ◽  
SANDER C. HILLE
Keyword(s):  
State Space ◽  
Metric Spaces ◽  
Transition Probabilities ◽  
Polish Space ◽  
Invariant Probability Measure ◽  
The State ◽  
Probability Measures ◽  
Ergodic Decomposition ◽  
Polish Spaces ◽  
Appl Math

AbstractFor any regular Markov operator on the space of finite Borel measures on a Polish space we give a Yosida-type decomposition of the state space, which yields a parametrization of the ergodic probability measures associated with this operator in terms of particular subsets of the state space. We use this parametrization to prove an integral decomposition of every invariant probability measure in terms of the ergodic probability measures and give an ergodic decomposition of the state space. This extends results by Yosida [Functional Analysis. Springer, Berlin, 1980, Ch. XIII.4], Hernández-Lerma and Lasserre [Ergodic theorems and ergodic decomposition for Markov chains. Acta Appl. Math.54 (1998), 99–119] and Zaharopol [An ergodic decomposition defined by transition probabilities. Acta Appl. Math.104 (2008), 47–81], who considered the setting of locally compact separable metric spaces. Our extension to Polish spaces solves an open problem posed by Zaharopol (loc. cit.) in a satisfactory manner.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

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