A non-commutative Path Space approach to stationary free Stochastic Differential Equations

Understand

By defining tracial states on a non-commutative analogue of a path space, we construct Markov dilations for a class of conservative completely Markov semigroups on finite von Neumann algebras.

• This class includes all symmetric semigroups.
• For well chosen semigroups (for instance with generator any divergence form operator associated to a derivation valued in the coarse correspondence) those dilations give rise to stationary solutions of certain free SDEs previously considered by D.
• Shlyakhtenko.