Artículos de revistas
Random Lie-point Symmetries
Registro en:
Journal Of Nonlinear Mathematical Physics. Lulea University Of Technology, v. 21, n. 2, p. 149 - 165, 2014.
14029251
10.1080/14029251.2014.900984
2-s2.0-84900427211
Autor
Catuogno P.J.
Lucinger L.R.
Institución
Resumen
We introduce the notion of a random symmetry. It consists of taking the action given by a deterministic flow that maintains the solutions of a given differential equation invariant and replacing it with a stochastic flow. This generates a random action, which we call a random symmetry. © 2014 Copyright: the authors. 21 2 149 165 Albeverio, S., Fei, S.-M., A remark on symmetry of stochastic dynamical systems and their conserved quantities (1995) J. Phys. A, 28 (22), pp. 6363-6371 Arnold, L., Imkeller, P., Normal forms for stochastic differential equations (1998) Probab. Theory Relat. Fields, 110, pp. 559-588 Bluman, G.W., Anco, S.C., Symmetry and integration methods for differential equations (2002) Applied Mathematical Sciences, 154. , Springer-Verlag, New York Gaeta, G., Quintero, N.R., Lie-point symmetries and stochastic differential equations (1999) J. Phys. A: Math. Gen., 32, pp. 8425-8505 Gaeta, G., Lie-point symmetries and stochastic differential equations: II (2000) J. Phys. A: Math. Gen., 33, pp. 4883-4902 Grigoriev, Y.N., Ibragimov, N.H., Kovalev, V.F., Meleshko, S.V., Symmetries of integrodifferential equations. with applications in mechanics and plasma physics (2010) Lecture Notes in Physics, 806. , Springer, Dordrecht Ibragimov, N.H., Ünal, G., Jogréus, C., Approximate symmetries and conservation laws for Ito and Stratonovich dynamical systems (2004) J. Math. Anal. Appl., 297 (1), pp. 152-168 Kozlov, R., The group classification of a scalar stochastic differential equation (2010) J. Phys. A: Math. Theor., 43 (5), pp. 055202-055214 Kozlov, R., On Lie group classification of a scalar stochastic differential equation (2011) J. Nonlinear Math. Phys., 18 SUPPL. 1, pp. 177-187 Melnick, S.A., The group analysis of stochastic differential equations (2002) Ann. Univ. Sci. Budapest. Sect. Comput., 21, pp. 69-79 Misawa, T., New conserved quantities derived from symmetry for stochastic dynamical systems (1994) J. Phys. A: Math. Gen., 27 (20), pp. 777-782 Olver, P.J., Applications of Lie groups to differential equations (1993) Graduate Texts in Mathematics, 107. , (Springer-Verlag, New York) Oksendal, B., (1998) Stochastic Differential Equations. An Introduction with Applications, , Fifth edition, Universitext (Springer-Verlag, Berlin) Oksendal, B., When is a stochastic integral a time change of a diffusion? (1990) J. Theoret. Probab., 3 (2), pp. 207-226 Srihirun, B., Meleshko, S., Schulz, E., On the definition of an admitted Lie group for stochastic differential equations (2007) Commun. Nonlinear Sci. Numer. Simul., 12, pp. 1379-1389 Stephani, H., (1989) Differential Equations: Their Solution Using Symmetries, , Cambridge University Press Ünal, G., Symmetries of Ito and Stratonovich dynamical systems and their conserved quantities (2003) Nonlinear Dyn., 32, pp. 417-426 Wafo Soh, C., Mahomed, F.M., Integration of stochastic ordinary differential equations from a symmetry standpoint (2001) J. Phys. A: Math. Gen., 34, pp. 177-192