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

2026/07/20 by Paolo Muratore-Ginanneschi
Mathematics · Physics and Astronomy · #cond-mat.stat-mech #math-ph #math.MP #math.PR #quant-ph

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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.

Related

• Approximation Schemes for Path Integration on Riemannian Manifolds
• Stochastic geodesics
• Finite dimensional approximations to Wiener measure and path integral formulas on manifolds
• Stochastic manifolds
• Stochastic parallel transport on the Wasserstein space and equivariant diffusions on the group of diffeomorphisms over a closed Riemannian manifold