A note on symmetries of diffusions within a martingale problem approach

2017/07/01 by Francesco C. De Vecchi, Paola Morando, Stefania Ugolini · 11 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Calculus (dental) #Geometric Analysis and Curvature Flows #Geometry #Homogeneous space #Local martingale #Martingale (probability theory) #Mathematical economics #Mathematics #Pure mathematics #advanced mathematical theories #math.DG #math.PR

paper · pdf · doi:10.1142/s0219493719500114

published in Stochastics and Dynamics 19(02), 1950011 (World Scientific)

arxiv created 2017/07/01 · openalex publication_date 2018/04/04 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Itô integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes.

Citations

• Reduction and reconstruction of stochastic differential equations via symmetries

Cited by

• Symmetries of stochastic differential equations using Girsanov transformations
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps