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.

arXiv comment60 pages, no figures; to appear in "Mathematics in Engineering"

References in corpus (18)

• Conditional Lie-Bäcklund symmetry and reduction of evolution equations.
• A Remark on Symmetry of Stochastic Dynamical Systems and Their Conserved Quantities
• Partial Lie-point symmetries of differential equations
• Symmetry of stochastic non-variational differential equations
• Hopf bifurcation with additive noise
• Invariants at fixed and arbitrary energy. A unified geometric approach
• Symmetries of Stochastic Differential Equations: a geometric approach
• Reduction and reconstruction of stochastic differential equations via symmetries
• Random Lie-point symmetries of stochastic differential equations
• Symmetries of Stochastic Differential Equations using Girsanov transformations
• W-Symmetries of Ito stochastic differential equations
• A note on symmetries of diffusions within a martingale problem approach
• Configurational invariants of Hamiltonian systems
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps
• Asymptotic scaling in a model class of anomalous reaction-diffusion equations
• 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