Stochastic exponential of continuous semimartingales, stochastic logarithm, Lévy's characterization of standard Brownian motion, Girsanov's theorem, change of drift using Girsanov's theorem, Doob's upcrossing inequality, Doob's convergence theorems for submartingales, representation of Brownian local martingales, Kazamaki's and Novikov's criterion, stochastic differential equations (examples, terminology, solution in the linear case), Ornstein–Uhlenbeck process, extended Grönwall inequality, existence and uniqueness of strong solutions under Lipschitz and boundedness conditions, moment estimates.