On stochastic deformations of dynamical systems

Journal of Nonlinear Mathematical Physics

Volumn 17, Issue SUPPL. 1, 2010, Pages 71-85

  Shereshevskii, Ilya ^a  

^a INSTITUTE FOR PHYSICS OF MICROSTRUCTURES   (Russian Federation)

Author keywords

Gibbs distribution; Stochastic equations

Indexed keywords

EID: 79551654574     PISSN: 14029251     EISSN: None     Source Type: Journal    
DOI: 10.1142/S1402925110000805     Document Type: Article

References (14)

1. E. Wong and M. Zakai, On the convergence of ordinary integrals to stochatic integrals, Ann. Math. Statist. 36(5) (1965) 1560-1564.
2. F. Guillermo,Wong-Zakai-Type theorem for certain discontinuouse semimartingals, J. Theoret. Probab. 2(3) (1989) 313-323.
3. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics. Vol. 9, Statistical Physics. Part 2 (Butterworth-Heinemann, 1980).
4. A. D. Wentzel, The Course of the Random Processes Theory (Nauka, Moscow, 1975) (in Russian).
5. R. L. Stratanovich, Conditional Markoff Processes and their Applications to Optimal Control Theory (MGU, Moscow, 1965) (in Russian).
6. R. L. Stratanovich, A new form of representing stochastic integrals and equations, Vestnik Moscov. Univ. Ser. I Math. Mech. 1 (1964) 3-12 (in Russian).
7. K. Chjun and R. Willams, Introduction to the Stochastic Integration (Mir, Moscow, 1987) (in Russian).
8. D. F. Kuznetsov, Numerical simulation of the stochastic differential equations and stochastic integrals, S-Pb GTU, (1998) (http://www.neva.ru/ journal) (in Russian).
9. L. John, Jr. Wyatt and G. J. Coram, Nonlinear device noise models: Satisfying the thermodynamic requirements, IEEE Trans. Electron Devices 46(1) (1999) 184-193.
10. Yu. E. Gliklikh, Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics, Mathematics and Its Applications, Vol. 374 (Springer, 1996).
11. L. C. Evans, An Introduction to Stochastic Differential Equations, http://www.rpi.edu/pearsy/ sde.pdf.
12. A. D. Wentzel and B. Freidlin, Dynamic Systems Under the Influence of Small Random Perturbations (Nauka, Moscow, 1970) (in Russian).
13. P. Ao, Emerging of stochastic dynamical equalities and steady state thermodynamics from Darwinian dynamics, Commun. Theor. Phys. (Beijing, China) 49 (2008) 1073-1090.
14. A. Hubert and R. Shäfer, Magnetic Domains (Springer-Verlag, Berlin Heidelberg, New York, 2000).