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

Paolo Muratore-Ginanneschi

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arXiv · 2607.17871

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

Paolo Muratore-Ginanneschi

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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.

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Paolo Muratore-Ginanneschi. 2026-07-20. On the use of the Belopol'skaya-Daletskii representation of a diffusion on a Riemann manifold to construct path integrals. https://arxiv.org/abs/2607.17871

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