Diagram Representation for the Stochastization of Single-Step Processes

  • Ekaterina G. Eferina
  • Michal Hnatich
  • Anna V. Korolkova
  • Dmitry S. KulyabovEmail author
  • Leonid A. Sevastianov
  • Tatiana R. Velieva
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 678)


Background. 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. Purpose. We want to get a unified abstract formalism for stochastization of one-step processes. This formalism should be equivalent to the previously introduced. Methods. To unify the methods of construction of the master equation, we propose to use the diagram technique. Results. We get a diagram technique, which allows to unify getting master equation for the system under study. We demonstrate the equivalence of the occupation number representation and the state vectors representation by using a Verhulst model. Conclusions. We have suggested a convenient diagram formalism for unified construction of stochastic systems.


Occupation numbers representation Fock space Dirac notation One-step processes Master equation Diagram technique 



The work is partially supported by RFBR grants No’s. 14-01-00628, 15-07-08795, and 16-07-00556. Also the publication was supported by the Ministry of Education and Science of the Russian Federation (the Agreement No. 02.a03.21.0008).


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Ekaterina G. Eferina
    • 1
  • Michal Hnatich
    • 3
    • 4
    • 5
  • Anna V. Korolkova
    • 1
  • Dmitry S. Kulyabov
    • 1
    • 2
    Email author
  • Leonid A. Sevastianov
    • 1
    • 3
  • Tatiana R. Velieva
    • 1
  1. 1.Department of Applied Probability and InformaticsRUDN University (Peoples’ Friendship University of Russia)MoscowRussia
  2. 2.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubna, Moscow RegionRussia
  3. 3.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubna, Moscow RegionRussia
  4. 4.Department of Theoretical PhysicsSAS, Institute of Experimental PhysicsKošiceSlovakia
  5. 5.Faculty of SciencePavol Jozef Šafárik University in Košice (UPJŠ)KošiceSlovakia

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