Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

Abstract

We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic one, such as conditional, partial and asymptotic symmetries. A number of explicit examples are presented.

60 pages, no figures; to appear in "Mathematics in Engineering"

References in corpus (7)

• Symmetry of stochastic non-variational differential equations
• Invariants at fixed and arbitrary energy. A unified geometric approach
• W-Symmetries of Ito stochastic differential equations
• Configurational invariants of Hamiltonian systems
• Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries
• Integration of the stochastic logistic equation via symmetry analysis
• Noether theorem in stochastic optimal control problems via contact symmetries