It is known that knowledge of a symmetry of a scalar Ito stochastic differential equations leads, thanks to the Kozlov substitution, to its integration. In the present paper we provide a classification of scalar autonomous Ito stochastic differential equations with simple noise possessing symmetries; here ``simple noise'' means the noise coefficient is of the form $\s (x,t) = s x^k$, with $s$ and $k$ real constants. Such equations can be taken to a standard form via a well known transformation; for such standard forms we also provide the integration of the symmetric equations. Our work extends previous classifications in that it also considers recently introduced types of symmetries, in particular standard random symmetries, not considered in those.
Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise / G. Gaeta, M. Angel Rodriguez. - In: OPEN COMMUNICATIONS IN NONLINEAR MATHEMATICAL PHYSICS. - 2:(2022), pp. ocnmp:9770.53-ocnmp:9770.101. [10.46298/ocnmp.9770]
Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise
G. GaetaCo-primo
;
2022
Abstract
It is known that knowledge of a symmetry of a scalar Ito stochastic differential equations leads, thanks to the Kozlov substitution, to its integration. In the present paper we provide a classification of scalar autonomous Ito stochastic differential equations with simple noise possessing symmetries; here ``simple noise'' means the noise coefficient is of the form $\s (x,t) = s x^k$, with $s$ and $k$ real constants. Such equations can be taken to a standard form via a well known transformation; for such standard forms we also provide the integration of the symmetric equations. Our work extends previous classifications in that it also considers recently introduced types of symmetries, in particular standard random symmetries, not considered in those.File | Dimensione | Formato | |
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