Reversible diffusion
In mathematics, a reversible diffusion is a specific example of a reversible stochastic process. Reversible diffusions have an elegant characterization due to the Russian mathematician Andrey Nikolaevich Kolmogorov.Kolmogorov's characterization of reversible diffusions
Let B denote a d-dimensional standard Brownian motion; let b : Rd → Rd be a Lipschitz continuous vector field. Let X : 0, +∞) × Ω → Rd be an [Itō diffusion defined on a probability space and solving the Itō stochastic differential equation
with square-integrable initial condition, i.e. X0 ∈ L2. Then the following are equivalent:
