Stochastization of one-step processes in the occupations number representation

By the means of the method of stochastization of one-step 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. © ECMS Thorsten Claus, Frank Herrmann, Michael Manitz, Oliver Rose (Editors).

Сборник материалов конференции
European Council for Modelling and Simulation
  • 1 Department of Applied Probability and Informatics, Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
  • 2 Institute of Informatics Problems, FRC CSC RAS, 44-2 Vavilova Str., Moscow, 119333, Russian Federation
  • 3 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, Dubna, Moscow region, 141980, Russian Federation
  • 4 Laboratory of Information Technologies, Joint Institute for Nuclear Research, Joliot-Curie 6, Dubna, Moscow region, 141980, Russian Federation
Ключевые слова
Dirac notation; Fock space; Master equation; Occupation numbers representation; One-step processes; Stochastic differential equations
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