On the behaviour of a standard Markov transition function near t=0

1965 ◽  
Vol 3 (4) ◽  
pp. 276-278 ◽  
Author(s):  
David G. Kendall
Keyword(s):  
Transition Function ◽  
Markov Transition ◽  
Markov Transition Function

Large deviations and the Bayesian estimation of higher-order Markov transition functions

1996 ◽  
Vol 33 (1) ◽  
pp. 18-27 ◽  
Author(s):  
F. Papangelou
Keyword(s):  
Large Deviations ◽  
Bayesian Estimation ◽  
Transition Function ◽  
Higher Order ◽  
Positive Probability ◽  
State Spaces ◽  
Empirical Distributions ◽  
Transition Functions ◽  
Markov Transition ◽  
Finite State

In the Bayesian estimation of higher-order Markov transition functions on finite state spaces, a prior distribution may assign positive probability to arbitrarily high orders. If there are n observations available, we show (for natural priors) that, with probability one, as n → ∞ the Bayesian posterior distribution ‘discriminates accurately' for orders up to β log n, if β is smaller than an explicitly determined β0. This means that the ‘large deviations' of the posterior are controlled by the relative entropies of the true transition function with respect to all others, much as the large deviations of the empirical distributions are governed by their relative entropies with respect to the true transition function. An example shows that the result can fail even for orders β log n if β is large.

Large deviations and the Bayesian estimation of higher-order Markov transition functions

1996 ◽  
Vol 33 (01) ◽  
pp. 18-27
Author(s):  
F. Papangelou
Keyword(s):  
Large Deviations ◽  
Bayesian Estimation ◽  
Transition Function ◽  
Higher Order ◽  
Positive Probability ◽  
State Spaces ◽  
Empirical Distributions ◽  
Transition Functions ◽  
Markov Transition ◽  
Finite State

In the Bayesian estimation of higher-order Markov transition functions on finite state spaces, a prior distribution may assign positive probability to arbitrarily high orders. If there are n observations available, we show (for natural priors) that, with probability one, as n → ∞ the Bayesian posterior distribution ‘discriminates accurately' for orders up to β log n, if β is smaller than an explicitly determined β 0. This means that the ‘large deviations' of the posterior are controlled by the relative entropies of the true transition function with respect to all others, much as the large deviations of the empirical distributions are governed by their relative entropies with respect to the true transition function. An example shows that the result can fail even for orders β log n if β is large.

The amplitude transition function and the manual and oculomotor control systems.

1988 ◽  
Vol 104 (3) ◽  
pp. 363-372 ◽  
Author(s):  
Nicholas C. Barrett ◽  
Denis J. Glencross
Keyword(s):  
Control Systems ◽  
Transition Function ◽  
Oculomotor Control

Modeling a random sequence of extremes of loads for fatigue tests under irregular loading

2020 ◽  
pp. 13-19
Author(s):  
N.A. Mahutov ◽  
I.V. Gadolina ◽  
S.G. Lebedinskiy ◽  
E.S. Oganyan ◽  
A.A. Bautin
Keyword(s):  
Random Sequence ◽  
Fatigue Tests ◽  
Linear Hypothesis ◽  
Resource Estimation ◽  
Transition Matrices ◽  
Random Loading ◽  
Markov Transition ◽  
Random Nature ◽  
Irregular Loading ◽  
Markov Transition Matrices

Methods and approaches to tests under random loading are considered, their role is characterized. To ensure the random nature of loading, a modeling method based on Markov transition matrices and real processes recorded in operation is proposed. Keywords: random loading process, Markov repetition matrices, resource estimation, corrected linear hypothesis, parameter of completeness of the loading spectrum. [email protected]

scholarly journals Petri Net-Based Semi-Compiled Code Generation for Programmable Logic Controllers

2021 ◽  
Vol 11 (15) ◽  
pp. 7161
Author(s):  
Igor Azkarate ◽  
Mikel Ayani ◽  
Juan Carlos Mugarza ◽  
Luka Eciolaza
Keyword(s):  
Code Generation ◽  
Resource Sharing ◽  
Discrete Event ◽  
Transition Function ◽  
Discrete Event Dynamic Systems ◽  
Programmable Logic ◽  
External Software ◽  
Implementation Methodology ◽  
Event Dynamic ◽  
Step Transition

Industrial discrete event dynamic systems (DEDSs) are commonly modeled by means of Petri nets (PNs). PNs have the capability to model behaviors such as concurrency, synchronization, and resource sharing, compared to a step transition function chart or GRAphe Fonctionnel de Commande Etape Transition (GRAFCET) which is a particular case of a PN. However, there is not an effective systematic way to implement a PN in a programmable logic controller (PLC), and so the implementation of such a controller outside a PLC in some external software that will communicate with the PLC is very common. There have been some attempts to implement PNs within a PLC, but they are dependent on how the logic of places and transitions is programmed for each application. This work proposes a novel application-independent and platform-independent PN implementation methodology. This methodology is a systematic way to implement a PN controller within industrial PLCs. A great portion of the code will be validated automatically prior to PLC implementation. Net structure and marking evolution will be checked on the basis of PN model structural analysis, and only net interpretation will be manually coded and error-prone. Thus, this methodology represents a systematic and semi-compiled PN implementation method. A use case supported by a digital twin (DT) is shown where the automated solution required by a manufacturing system is carried out and executed in two different devices for portability testing, and the scan cycle periods are compared for both approaches.

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