RUS  ENG
Полная версия
ЖУРНАЛЫ // Фундаментальная и прикладная математика

Фундамент. и прикл. матем., 2015, том 20, выпуск 3, страницы 213–249 (Mi fpm1660)

Редукция и интегрируемость стохастических динамических систем
Нгуен Тьен Зунг, Нгуен Тхань Тхьен

Литература

1. Albeverio S., Fei S., “Remark on symmetry of stochastic dynamical systems and their conserved quantities”, J. Phys. A, 28 (1995), 6363–6371  crossref  mathscinet  zmath  isi
2. Bismut J. M., Mecanique Aleatoire, Lect. Notes Math., 866, Springer, Berlin, 1981  crossref  mathscinet  zmath
3. Błaszak M, Domański Z., Sergyeyev A., Szablikowski B., “Integrable quantum Stäckel systems”, Phys. Lett. A, 377:38 (2013), 2564–2572  crossref  mathscinet
4. Bolsinov A. V., Matveev V. S., “Geometrical interpretation of Benenti systems”, J. Geom. Phys., 44:4 (2003), 489–506  crossref  mathscinet  zmath  isi
5. Borodin A. N., Freidlin M. I., “Fast oscillating random perturbations of dynamical systems with conservation laws”, Ann. Inst. H. Poincaré Probab. Statist., 31:3 (1995), 485–525  mathscinet  zmath
6. Duval C., Valent G., “Quantum integrability of quadratic Killing tensors”, J. Math. Phys., 46:5 (2005), 053516  crossref  mathscinet  zmath  isi
7. Fomenko A. T., Bolsinov A. V., Integrable Hamiltonian Systems: Geometry, Topology, Classification, Chapman & Hall/CRC, Boca Raton, 2004  mathscinet  zmath
8. Freidlin M., Weber M., “Random perturbations of dynamical systems and diffusion processes with conservation laws”, Probab. Theory Related Fields, 128:3 (2004), 441–466  crossref  mathscinet  zmath  isi
9. Galmarino A. R., “Representation of an isotropic diffusion as a skew product”, Z. Wahrsch. Verw. Gebiete, 1:4 (1963), 359–378  crossref  mathscinet  zmath
10. Gitterman M., The Noisy Oscillator: The First Hundred Years, from Einstein Until Now, World Scientific, New York, 2005  mathscinet  zmath
11. Grove K., Karcher H., Ruh E. A., “Group actions and curvature”, Invent. Math., 23 (1974), 31–48  crossref  mathscinet  zmath
12. Ikeda N., Watanabe S., Stochastic Differential Equations and Diffusion Processes, North-Holland Math. Lib., 24, North-Holland, 1981  mathscinet  zmath
13. Jovanovic B., “Symmetries and integrability”, Publ. Inst. Math. (Beograd), 84(98) (2008), 1–36  crossref  mathscinet  zmath
14. Kunita H., Stochastic Flows and Stochastic Differential Equations, Cambridge Univ. Press, Cambridge, 1997  mathscinet  zmath
15. Lázaro-Camí J.-A., Ortega J.-P., “Reduction, reconstruction, and skew-product decomposition of symmetric stochastic differential equations”, Stoch. Dyn., 9:1 (2009), 1–46  crossref  mathscinet  zmath  isi
16. Li Xue-Mei, “An averaging principle for a completely integrable stochastic Hamiltonian system”, Nonlinearity, 21:4 (2008), 803–822  crossref  mathscinet  zmath  isi
17. Liao M., “A decomposition of Markov processes via group action”, J. Theor. Probab., 22:1 (2009), 164–185  crossref  mathscinet  zmath  isi
18. Liouville J., “Note sur l'intégration des équations différentielles de la dynamique”, J. Math. Pures Appl., 20 (1855), 137–138
19. Markus L., Weerasinghe A., “Stochastic oscillators”, J. Differ. Equ., 71:2 (1988), 288–314  crossref  mathscinet  zmath  isi
20. Matveev V. S., “Quantum integrability of the Beltrami–Laplace operator for geodesically equivalent metrics”, Russ. Math. Dokl., 61:2 (2000), 216–219  mathscinet  zmath
21. Misawa T., “Conserved quantities and symmetries related to stochastic dynamical systems”, Ann. Inst. Stat. Math., 51:4 (1999), 779–802  crossref  mathscinet  zmath  isi
22. Øksendal B., Stochastic Differential Equations, Springer, Berlin, 2003  mathscinet
23. Pauwels E. J., Rogers L. C. G., “Skew-product decompositions of Brownian motions”, Contemp. Math., 73 (1988), 237–262  crossref  mathscinet  zmath
24. Taylor M., Pseudodifferential Operators, Springer, New York, 1996  mathscinet
25. Zung N. T., “Torus actions and integrable systems”, Topological Methods in the Theory of Integrable Systems, Cambridge Sci. Publ., Cambridge, 2006, 289–328  mathscinet  zmath
26. Zung N. T., A general approach to the problem of action-angle variables, In preparation; Earlier version: Action-angle variables on Dirac manifolds, arXiv: 1204.3865
27. Zung N. T., Thien N. T., Physics-like second-order models of financial assets prices, In preparation


© МИАН, 2025