“…This result paves the way for the proof of Theorem 3.15, the second result of this paper, where a Chernoff approximation formula (Equation (3.12)) for the Feller semigroup in terms of a family of rather simple shift operators is presented. The idea of using shift operators instead of integral operators on
goes back to [
46–48, 59] and is now applied to manifolds for the first time. We also extend the described results to more general operators
, where c is a bounded continuous scalar potential.
- (b)The probabilistic interpretation of the approximation formulas (3.10) and (3.12) in the case of is discussed in Section 4.
…”