2022
DOI: 10.48550/arxiv.2207.02780
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Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise

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 σ(x, t) = sx 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 … Show more

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