A reduction procedure for stochastic differential equations based on stochastic symmetries includingGirsanov 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
De Vecchi F. C.;
2021-01-01
Abstract
A reduction procedure for stochastic differential equations based on stochastic symmetries includingGirsanov 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.File in questo prodotto:
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