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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.
Versions
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BibTeX
@misc{muratoreginanneschi2026belopolskayadaletskii,
title = {{On the use of the Belopol'skaya-Daletskii representation of a diffusion on a Riemann manifold to construct path integrals}},
author = {Paolo Muratore-Ginanneschi},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.17871},
eprint = {2607.17871},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.17871},
}
RIS
TY - UNPB
TI - On the use of the Belopol'skaya-Daletskii representation of a diffusion on a Riemann manifold to construct path integrals
AU - Paolo Muratore-Ginanneschi
PY - 2026
DA - 2026/07/20
PB - arXiv
DO - 10.48550/arxiv.2607.17871
UR - https://arxiv.org/abs/2607.17871
AB - 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.
ER -