Reversibility for diffusions via quasi-invariance. (English) Zbl 1214.60038

Rivasplata, Omar; Rychtář, Jan; Schmuland, Byron

Acta Univ. Carol., Math. Phys. 48, No. 1, 3-10 (2007).

Summary: Why is the drift coefficient \(b\) associated with a reversible diffusion on \(\mathbb R^d\) given by a gradient? Our explanation is inspired by Handa’s recent results on reversibility and quasi-invariance of the invariant measure.

MSC:

60J60	Diffusion processes
28C10	Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
47F05	General theory of partial differential operators
47D07	Markov semigroups and applications to diffusion processes

Keywords:

diffusion process; infinitesimal generator; reversible measure; quasi-invariant measure; cocycle identity