A strong quasi-invariance principle and a finite-dimensional integration by parts formula as in the Bismut approach to Malliavin calculus are obtained through a suitable application of Lie symmetry theory to stochastic differential equations. The main stochastic, geometrical and analytical aspects of the theory are discussed and applications to some Brownian motion driven stochastic models are provided.
Integration by parts formulas and Lie symmetries of SDEs / F.C. De Vecchi, P. Morando, S. Ugolini. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - 30:(2025), pp. 86.1-86.41. [10.1214/25-ejp1349]
Integration by parts formulas and Lie symmetries of SDEs
F.C. De Vecchi
Primo
;P. MorandoSecondo
;S. UgoliniUltimo
2025
Abstract
A strong quasi-invariance principle and a finite-dimensional integration by parts formula as in the Bismut approach to Malliavin calculus are obtained through a suitable application of Lie symmetry theory to stochastic differential equations. The main stochastic, geometrical and analytical aspects of the theory are discussed and applications to some Brownian motion driven stochastic models are provided.
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