Group classification of the linear stochastic differential ito equation
Keywords:
stochastic differential Ito equation, group analysis, commutator, Lie operation algebraAbstract
The article deals with the task on the group classification of the linear stochastic differential Ito equation of a given type which changes due to the parameters appearing in this equation. The problem is solved by the symmetry reduction. The result of the study is a table full of group classification of the equations, which lists all the possible equations and allowed their symmetry groupReferences
Lie. S. Classification und Integration won gewonlichen Differentialgleichungen zwischen x, y, die eine Gruppe von Transformationen gestatten / S. Lie.// Math. Ann. – 1888. – Vol. 32. – P. 213–281.
Lie S. Vorlesungen über continuierliche Gruppen / S. Lie. – Leipzig: B.G. Teubner, 1893. – 805 p.
Lie S. Vorlesungen über Differential geichungen mit bekannten infinitesimalen Transformationen / S. Lie. – Leipzig: B.G. Teubner, 1891. – 800 p.
Lagno V. I. Symmetry analysis of the evolution equations / V. I. Lagno, S. V. Spichack, V. I. Stogniy. – MoscowIzhevsck: Institute of Computer Investigations, 2004. – 392 p.
Buchnev A. A. Lie group admitted by the equations of perfect incompressible liquid motion / A. A. Buchnev // Continuum dynamics, Vol. 7. – Novosibirsk, 1971. – P. 212–214.
Bytev V. O. Group properties of the Navier-Stokes equations // V. O. Bytev // Numerical methods of continuum mechanics. – Novosibirsk: Computer Center of the Siberian Dept. of the USSR Acad. of Sciences, 1975. – Vol. 3, No 5. – P. 13–17.
Ibragimov N. Kh. Group properties of wave equations for zero mass particles / N. Kh. Ibragimov. – Proc. Of the USSR Acad. of Sciences. – 1968. – Vol. 178, No 3. – 48 p.
Daletsky Yu. L. Stochastic equations and differential geometry / Yu. L. Daletsky, Ya. I. Belopol’skaya. – K.: Higher School, 1989. – 395 p.
Melnik S. A. The group analysis of the stochastic differential equation / S. A. Melnik // J. Annals Univ. Sci. Budapest, Sect. Comp. – 2002. – Vol. 21. – P. 7–12.
Gaeta G. Lie point symmetries and stochastic differential equations / G. Gaeta, N. Rodriguez Quinterro // J. Phys. Math. Gen. – 1999. – Vol. 32. – P. 8485–8505.
Gaeta G. Lie point symmetries and stochastic differential equations II / G. Gaeta // J. Phys. Math. Gen. – 2000. – Vol. 33. – P. 4883–4902.
Gaeta G. Symmetry of Stochastic Equations / G. Gaeta // Proceedings of Institute of Mathematics of NAS of Ukraine. – 2004. – Vol. 50, Part 1. – P. 98–109.
Alexandrova O. V. Group analysis of the Ito Stochastic system / O. V. Alexandrova // Differential Equations and Dynamical Systems. – 2006. – Vol. 14, No 3/4. – P. 255–279.
Alexandrova O. V. Symmetry and first integrals of the systems of stochastic differential Ito equations / O. V. Alexandrova // Vestnik of NovSU named after Yaroslav the Wise – Ser.: Physical and mathematical sciences, 2013. – No 76, Vol. 1. – P. 54–60.
Ibragimov N. Kh. Group analysis experience / N. Kh. Ibragimov. – M.: Znanie: The new in life, science and engineering, 1989. – No 9. – 45 p.