Digital Library of the European Council for Modelling and Simulation

Title:	Stochastization Of One-Step Processes In The Occupations Number Representation
Authors:	Anna V. Korolkova, Ekaterina G. Eferina, Eugeny B. Laneev, Irina A. Gudkova, Leonid A. Sevastianov, Dmitry S. Kulyabov
Published in:	(2016).ECMS 2016 Proceedings edited by: Thorsen Claus, Frank Herrmann, Michael Manitz, Oliver Rose, European Council for Modeling and Simulation. doi:10.7148/2016 ISBN: 978-0-9932440-2-5 30^th European Conference on Modelling and Simulation, Regensburg Germany, May 31^st – June 3^rd, 2016
Citation format:	Anna V. Korolkova, Ekaterina G. Eferina, Eugeny B. Laneev, Irina A. Gudkova, Leonid A. Sevastianov, Dmitry S. Kulyabov (2016). Stochastization Of One-Step Processes In The Occupations Number Representation, ECMS 2016 Proceedings edited by: Thorsten Claus, Frank Herrmann, Michael Manitz, Oliver Rose European Council for Modeling and Simulation. doi:10.7148/2016-0698
DOI:	http://dx.doi.org/10.7148/2016-0698
Abstract:	By the means of the method of stochastization of onestep processes we get the simplified mathematical model of the original stochastic system. We can explore these models by standard methods, as opposed to the original system. The process of stochastization depends on the type of the system under study. We want to get a unified abstract formalism for stochastization of one-step processes. This formalism should be equivalent to the previously introduced. To implement an abstract approach we use the representation of occupation numbers. In this presentation we use the operator formalism. A feature of this formalism is the use of abstract linear operators which are independent from the state vectors. We use the formalism of Green’s functions in order to deal with operators. We get a fully coherent formalism by using the occupation numbers representation. With its help we can get simplified stochastic model of the original system. We demonstrate the equivalence of the occupation number representation and the state vectors representation by using a one-step process example. We have suggested a convenient formalism for unified description of stochastic systems. Also, this method can be extended for the study of nonlinear stochastic systems.
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