Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries

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.

We have fixed an error in the proof of Proposition 24 (former Proposition 23) and corrected some typos

References in corpus (3)

• The calculation of expectations for classes of diffusion processes by Lie symmetry methods
• Symmetry of stochastic non-variational differential equations
• W-Symmetries of Ito stochastic differential equations

Cited by in corpus (5)

• Noether theorem in stochastic optimal control problems via contact symmetries
• Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise
• Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field
• On the integration of Ito equations with a random or a W-symmetry
• Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations