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

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.