A note on symmetries of diffusions within a martingale problem approach

Abstract

A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second order geometry and Ito integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes.

References in corpus (2)

• Symmetries of Stochastic Differential Equations: a geometric approach
• Reduction and reconstruction of stochastic differential equations via symmetries

Cited by in corpus (6)

• Symmetries of Stochastic Differential Equations using Girsanov transformations
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps
• Noether theorem in stochastic optimal control problems via contact symmetries
• 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