On the use of the Belopol'skaya-Daletskii representation of a diffusion on a Riemann manifold to construct path integrals

Abstract:We show that the Belopol'skaya-Daletskii formulation of stochastic differential equations on a Riemann manifold offers an elementary way to construct equivariant representations of finite-dimensional approximations to the path measure of a diffusion. The key ingredient is the use of the exponential map to describe increments of the diffusion.

Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Probability (math.PR); Quantum Physics (quant-ph)

arXiv:2607.17871 [cond-mat.stat-mech]

(or arXiv:2607.17871v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2607.17871 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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