Chernoff's theorem for backward propagators and applications to diffusions on manifolds

TL;DR

This paper generalizes Chernoff's theorem to backward propagators, providing a framework for discrete-time approximations of diffusions on manifolds, extending classical semigroup approximation results.

Contribution

It extends Chernoff's theorem to backward propagators, enabling better approximation of diffusions on manifolds in discrete time.

Findings

Generalized Chernoff's theorem for backward propagators

Established discrete-time approximation methods for diffusions on manifolds

Extended classical results to a broader class of semigroup approximations

Abstract

The classical Chernoff's theorem is a statement about discrete-time approximations of semigroups, where the approximations are consturcted as products of time-dependent contraction operators strongly differentiable at zero. We generalize the version of Chernoff's theorem for semigroups proved in a paper by Smolyanov et al., and obtain a theorem about descrete-time approximations of backward propagators.