7 Brownian motion and transition semigroups
The Markov property allows us to study Brownian motion through an analytic approach. For this we associate with a Brownian motion (Bt)t≥0 two families of linear operators, the (transition) semigroup
and the resolvent
Throughout this chapter we assume that (Bt)t≥0 is a d-dimensional Brownian motion which is adapted to the filtration . We will assume that is right-continuous, i. e. for all ...