Aiming at enlarging the class of symmetries of an SDE, we introduce a family of stochastic transformations able to change also the underlying probability measure exploiting Girsanov Theorem and we provide new determining equations for the infinitesimal symmetries of the SDE. The well-defined subset of the previous class of measure transformations given by Doob transformations allows us to recover all the Lie point symmetries of the Kolmogorov equation associated with the SDE. This gives the first stochastic interpretation of all the deterministic symmetries of the Kolmogorov equation. The general theory is applied to some relevant stochastic models.

Symmetries of stochastic differential equations using Girsanov transformations / F.C. De Vecchi, P. Morando, S. Ugolini. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 53:13(2020 Apr 03). [10.1088/1751-8121/ab757d]

Symmetries of stochastic differential equations using Girsanov transformations

Morando, Paola;Ugolini, Stefania
2020-04-03

Abstract

Aiming at enlarging the class of symmetries of an SDE, we introduce a family of stochastic transformations able to change also the underlying probability measure exploiting Girsanov Theorem and we provide new determining equations for the infinitesimal symmetries of the SDE. The well-defined subset of the previous class of measure transformations given by Doob transformations allows us to recover all the Lie point symmetries of the Kolmogorov equation associated with the SDE. This gives the first stochastic interpretation of all the deterministic symmetries of the Kolmogorov equation. The general theory is applied to some relevant stochastic models.
stochastic differential equations; Kolmogorov equation; Girsanov transformations; Doob h-transforms; lie symmetry analysis;
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore MAT/07 - Fisica Matematica
12-feb-2020
JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/720909
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