
Digital
Library of the European Council for Modelling and Simulation 
Title: 
Stochastization Of OneStep 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:
9780993244025 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 OneStep 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:10.7148/20160698 
DOI: 
http://dx.doi.org/10.7148/20160698 
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 onestep
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 onestep 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. 
Full
text: 