@article{UFA_2015_7_3_a4,
author = {V. V. Davydovych},
title = {Preliminary group classification of $(2+1)$-dimensional linear ultraparabolic {Kolmogorov{\textendash}Fokker{\textendash}Planck} equations},
journal = {Ufa mathematical journal},
pages = {38--46},
year = {2015},
volume = {7},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a4/}
}
TY - JOUR AU - V. V. Davydovych TI - Preliminary group classification of $(2+1)$-dimensional linear ultraparabolic Kolmogorov–Fokker–Planck equations JO - Ufa mathematical journal PY - 2015 SP - 38 EP - 46 VL - 7 IS - 3 UR - http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a4/ LA - en ID - UFA_2015_7_3_a4 ER -
V. V. Davydovych. Preliminary group classification of $(2+1)$-dimensional linear ultraparabolic Kolmogorov–Fokker–Planck equations. Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 38-46. http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a4/
[1] C. W. Gardiner, Handbook of stochastic methods, Springer, Berlin, 1985 | MR
[2] A. N. Kolmogoroff, “Zufällige Bewegungen (Zur Theorie der Brownschen Bewegung)”, Ann. Math., 35:1 (1934), 116–117 | DOI | MR | Zbl
[3] P. Wilmott, S. Howison, J. Dewynne, Option pricing: mathematical models and computation, Oxford financial press, 1993
[4] A. Pascucci, “Kolmogorov equations in physics and in finance”, Prog. Nonlinear Differential Equations Appl., 63 (2005), 353–364 | DOI | MR | Zbl
[5] H. Geman, M. Yor, “Bessel processes, Asian options, and perpetuities”, Math. Fin., 3:4 (1993), 349–375 | DOI | Zbl
[6] W. M. Shtelen, V. I. Stogny, “Symmetry properties of one- and two-dimensional Fokker–Planck equations”, J. Phys. A: Math. Gen., 22:13 (1989), L539 | DOI | MR | Zbl
[7] S. Spichak, V. Stogny, “Symmetry analysis of the Kramers equation”, Rep. Math. Phys., 40:1 (1997), 125–130 | DOI | MR | Zbl
[8] S. V. Spichak, V. I. Stogniy, I. M. Kopas, “Symmetry properties and exact solutions of the linear Kolmogorov equation”, Research Bulletin of NTUU “Kyiv Polytechnic Institute”, 2011, no. 4, 93–97 (in Ukrainian)
[9] S. S. Kovalenko, I. M. Kopas, V. I. Stogniy, “Preliminary group classification of a class of generalized linear Kolmogorov equations”, Research Bulletin of NTUU “Kyiv Polytechnic Institute”, 2013, no. 4, 67–72 (in Ukrainian)
[10] E. Barucci, S. Polidoro, V. Vespri, “Some results on partial differential equations and Asian options”, Math. Models Methods Appl. Sci., 11:3 (2001), 475–497 | DOI | MR | Zbl
[11] R. Z. Zhdanov, V. I. Lahno, “Group classification of heat conductivity equations with a nonlinear source”, J. Phys. A: Math. Gen., 32:42 (1999), 7405 | DOI | MR | Zbl
[12] Lagno V. I., Spichak S. V., Stognii V. I., Simmetriinyi analiz uravnenii evolyutsionnogo tipa, Institut kompyuternykh issledovanii, Izhevsk, 2004, 392 pp.
[13] P. Basarab-Horwath, V. Lahno, R. Zhdanov, “The structure of Lie algebras and the classification problem for partial differential equations”, Acta Applicandae Mathematica, 69:1 (2001), 43–94 | DOI | MR | Zbl
[14] V. Lahno, R. Zhdanov, “Group classification of nonlinear wave equations”, J. Math. Phys., 46:5 (2005), 053301 | DOI | MR | Zbl
[15] R. Zhdanov, V. Lahno, “Group classification of the general second-order evolution equation: semi-simple invariance groups”, J. Phys. A: Math. Theor., 40:19 (2007), 5083 | DOI | MR | Zbl
[16] Q. Huang, V. Lahno, C. Z. Qu, R. Zhdanov, “Preliminary group classification of a class of fourth-order evolution equations”, J. Math. Phys., 50:2 (2009), 023503 | DOI | MR | Zbl
[17] D.-j. Huang, H.-q. Zhang, “Preliminary group classification of quasilinear third-order evolution equations”, Appl. Math. Mech., 30 (2009), 275–292 | DOI | MR | Zbl
[18] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR
[19] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR
[20] G. W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York, 1989 | MR | Zbl
[21] P. J. Olver, Applications of Lie groups to differential equations, Springer, Berlin, 1986 | MR | Zbl
[22] Mubarakzyanov G. M., “O razreshimykh algebrakh Li”, Izv. vyssh. uchebn. zaved. Matematika, 1963, no. 1, 114–123 | MR | Zbl