A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of functionals of solution to the SDE and a reconstruction theorem for general stochastic symmetries is proved. Moreover, the notable case of reduction under the closed subclass of quasi Doob transformations is presented. The theoretical results are applied to stochastic models relevant in the applications

Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries / F.C. De Vecchi, P. Morando, S. Ugolini. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 54:18(2021), pp. 185203.1-185203.33. [10.1088/1751-8121/abef7f]

Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries

P. Morando;S. Ugolini
2021

Abstract

A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of functionals of solution to the SDE and a reconstruction theorem for general stochastic symmetries is proved. Moreover, the notable case of reduction under the closed subclass of quasi Doob transformations is presented. The theoretical results are applied to stochastic models relevant in the applications
Lie’s symmetry analysis, stochastic differential equations, Girsanov transform, Doob’s h-transform, integration by quadratures
Settore MAT/07 - Fisica Matematica
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/839713
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