Random rotational invariance of integration by parts formulas within a Bismut-type approach

2025/06/13 by Susanna Dehò, Francesco C. De Vecchi, Dehò, Susanna +5
Computer Science · #58D19 #60H07 #60H10 #Bayesian Methods and Mixture Models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2506.11937

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect of the rotational invariance of the driving Brownian motion in the derivation of the integration by parts formula is discussed and the invariance property of the formula is shown via applications to some explicit two-dimensional Brownian motion-driven stochastic models.

Citations

• Random transformations and invariance of semimartingales on Lie groups
• Reduction, reconstruction, and skew-product decomposition of symmetric stochastic differential equations

Related

• Integration by parts formulas and Lie's symmetries of SDEs
• Random transformations and invariance of semimartingales on Lie groups
• Schur-Weyl duality and the Product of randomly-rotated symmetries by a unitary Brownian motion
• The Bismut-Elworthy-Li formula for mean-field stochastic differential\n equations
• Bismut formulae and applications for stochastic (functional) differential equations driven by fractional Brownian motions