Symmetry classification of scalar Ito equations with multiplicative noise

References

• G. Gaeta, Integration of the stochastic logistic equation via symmetry analysis, J. Nonlin. Math. Phys., 26 (2019) 454–467. doi: 10.1080/14029251.2019.1613052
   Web of Science ®Google Scholar
• O. Ovaskainen and B. Meerson, Stochastic models of population extinction, Trends in Ecology and Evolution, 25 (2010) 643–652; arXiv:1008.1162 doi: 10.1016/j.tree.2010.07.009
   PubMed Web of Science ®Google Scholar
• B. Spagnolo, D. Valenti and A. Fiasconaro, Noise in Ecosystems: a short review, Math. Biosci. Eng., 1 (2004) 185–211; arXiv:q-bio/0403004 doi: 10.3934/mbe.2004.1.185
   PubMed Web of Science ®Google Scholar
• G. Gaeta and N. Rodríguez-Quintero, Lie-point symmetries and stochastic differential equations, J. Phys. A, 32 (1999) 8485–8505. doi: 10.1088/0305-4470/32/48/310
   Google Scholar
• G. Gaeta, Lie-point symmetries and stochastic differential equations II, J. Phys. A, 33 (2000) 4883– 4902. doi: 10.1088/0305-4470/33/27/306
   Google Scholar
• G. Unal, Symmetries of Ito and Stratonovich dynamical systems and their conserved quantities, Nonlin. Dyn., 32 (2003) 417–426. doi: 10.1023/A:1025669920594
   Web of Science ®Google Scholar
• R. Kozlov, Symmetry of systems of stochastic differential equations with diffusion matrices of full rank, J. Phys. A, 43 (2010) 245201. doi: 10.1088/1751-8113/43/24/245201
   Google Scholar
• R. Kozlov, The group classification of a scalar stochastic differential equations, J. Phys. A, 43 (2010) 055202. doi: 10.1088/1751-8113/43/5/055202
   Google Scholar
• R. Kozlov, On maximal Lie point symmetry groups admitted by scalar stochastic differential equations, J. Phys. A, 44 (2011) 205202. doi: 10.1088/1751-8113/44/20/205202
   Google Scholar
• G. Gaeta and F. Spadaro, Random Lie-point symmetries of stochastic differential equations, J. Math. Phys. 58 (2017), 053503 [Erratum, J. Math. Phys., 58 (2017), 129901] doi: 10.1063/1.4982639
   Web of Science ®Google Scholar
• G. Gaeta, Symmetry of stochastic non-variational differential equations, Phys. Rep. 686 (2017), 1–62 [Erratum: 713, 18]. doi: 10.1016/j.physrep.2017.05.005
   Google Scholar
• G. Gaeta and C. Lunini, On Lie-point symmetries for Ito stochastic differential equations, J. Nonlin. Math. Phys., 24-S1 (2017) 90–102. doi: 10.1080/14029251.2017.1418056
   Web of Science ®Google Scholar
• G. Gaeta and C. Lunini, Symmetry and integrability for stochastic differential equations, J. Nonlin. Math. Phys., 25 (2018) 262–289. doi: 10.1080/14029251.2018.1452673
   Web of Science ®Google Scholar
• R. Kozlov, Random Lie symmetries of Ito stochastic differential equations, J. Phys. A, 51 (2018) 305203. doi: 10.1088/1751-8121/aac95a
   Google Scholar
• R. Kozlov, Lie-point symmetries of Stratonovich stochastic differential equations, J. Phys. A, 51 (2018) 505201. doi: 10.1088/1751-8121/aae753
   Google Scholar
• R. Kozlov, Symmetries of Ito stochastic differential equations and their applications, in Nonlinear systems and their remarkable mathematical structures, N. Euler ed., CRC Press 2018.
   Google Scholar
• G. Gaeta, C. Lunini and F. Spadaro, Recent advances in symmetry of stochastic differential equations, Rend. Mat. Appl., 39 (2018) 293–306.
   Google Scholar
• G. Gaeta, W-Symmetries of Ito stochastic differential equations, J. Math. Phys., 60 (2019) 053501. doi: 10.1063/1.5080434
   Web of Science ®Google Scholar
• D.V. Alexseevsky, A.M. Vinogradov and V.V. Lychagin, Basic Ideas and Concepts of Differential Geometry, (Springer, 1991).
   Google Scholar
• G. Cicogna and G. Gaeta, Symmetry and Perturbation Theory in Nonlinear Dynamics, (Springer, 1999).
   Google Scholar
• I.S. Krasil’schik and A.M. Vinogradov, Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, (A.M.S., 1999).
   Google Scholar
• P.J. Olver, Application of Lie Groups to Differential Equations, (Springer, 1986).
   Google Scholar
• P.J. Olver, Equivalence, Invariants and Symmetry, (Cambridge University Press, 1995).
   Google Scholar
• H. Stephani, Differential Equations. Their Solution Using Symmetries, (Cambridge University Press, 1989).
   Google Scholar
• L. Arnold, Random Dynamical Systems, (Springer, 1988).
   Google Scholar
• L.C. Evans, An Introduction to Stochastic Differential Equations, (A.M.S., 2013).
   Google Scholar
• D. Freedman, Brownian Motion and Diffusion, (Springer, 1983).
   Google Scholar
• N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, (North Holland, 1981).
   Google Scholar
• N.G. van Kampen, Stochastic Processes in Physics and Chemistry, (North Holland 1992; 2003).
   Google Scholar
• B. Oksendal, Stochastic Differential Equations (4th edition), (Springer, 1985).
   Google Scholar
• D.W. Stroock, Markov Processes from K.Ito’s Perspective, Princeton UP 2003
   Google Scholar
• G. Gaeta and F. Spadaro, arXiv:2002.05122
   Google Scholar