LABOUR ALLOCATION POLICIES BASED ON SEMI-MARTINGALE METHODS

Introduction. The article deals with mathematical models of two main classes of processes in stochastic productive systems. For a multistage system, conditions of belonging to a “just-in-time” class or a class with infinite support of the time distribution function for productive operations are determined. Materials and Methods. Descriptions and investigations of models are carried out by trajectory (martingale) methods. For “just-in-time” systems and multistage stochastic productive systems, terms and methods of random walks in a random environment and birth and death processes are used. The results are formulated as descriptions of intensity characteristics of equalizers of point counting processes. Results. Two theorems are given and proved; they justify the proposed classification of the mathematical models of productive systems. The criteria of the belonging of the stochastic productive system to the class “just-in-time” are given. A theorem on the incompatibility of groups of “just-in-time” systems and systems infinite support of the time distribution for operations is proved. Discussion and Conclusion. The results show the feasibility of analyzing stochastic productive systems by martingale methods. The descriptions of terms of intensities of the equalizers time of productive processes admit generalization.

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Right Censoring and Martingale Methods for Failure Time Data

The Annals of Statistics ◽

10.1214/aos/1176347260 ◽

1989 ◽

Vol 17 (3) ◽

pp. 1133-1156 ◽

Cited By ~ 13

Author(s):

Martin Jacobsen

Keyword(s):

Failure Time ◽

Right Censoring ◽

Failure Time Data ◽

Time Data ◽

Martingale Methods

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Martingale Methods for the Central Limit Theorem

Rabi N. Bhattacharya ◽

10.1007/978-3-319-30190-7_5 ◽

2016 ◽

pp. 131-135

Author(s):

S. R. Srinisava Varadhan

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

The Central Limit Theorem ◽

Martingale Methods

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Estimation of the Malthusian parameter in an stochastic epidemic model using martingale methods

Mathematical Biosciences ◽

10.1016/j.mbs.2013.10.002 ◽

2013 ◽

Vol 246 (2) ◽

pp. 272-279 ◽

Cited By ~ 4

Author(s):

David Lindenstrand ◽

Åke Svensson

Keyword(s):

Epidemic Model ◽

Malthusian Parameter ◽

Martingale Methods ◽

Stochastic Epidemic ◽

Stochastic Epidemic Model

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6. Martingale Methods

Empirical Processes with Applications to Statistics ◽

10.1137/1.9780898719017.ch6 ◽

2009 ◽

pp. 258-292

Keyword(s):

Martingale Methods

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A bivariate counting process

Journal of Applied Probability ◽

10.2307/3214844 ◽

1993 ◽

Vol 30 (2) ◽

pp. 353-364 ◽

Cited By ~ 3

Author(s):

Ray Watson ◽

Paul Yip

Keyword(s):

Epidemic Model ◽

Time Scale ◽

Counting Process ◽

Transition Probabilities ◽

Random Time ◽

Scale Transformation ◽

Asymptotic Results ◽

Martingale Methods ◽

Conflict Model ◽

Population Processes

We consider a bivariate Markov counting process with transition probabilities having a particular structure, which includes a number of useful population processes. Using a suitable random time-scale transformation, we derive some probability statements about the process and some asymptotic results. These asymptotic results are also derived using martingale methods. Further, it is shown that these methods and results can be used for inference on the rate parameters for the process. The general epidemic model and the square law conflict model are used as illustrative examples.

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