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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 (B_t)_t≥0 two families of linear operators, the (transition) semigroup

(7.1)

and the resolvent

(7.2)

Throughout this chapter we assume that (B_t)_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 ...

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