Discrete dynamical models (covered quietly):

Markov chains, one dimensional and multidimensional trees, forward and backward difference equations, transition probabilities and conditional expectations, algebras of sets of paths representing partial information, martingales and stopping times.

Continuous processes in continuous time:

Brownian motion, Ito integral and Ito's lemma, forward and backward partial differential equations for transition probabilities and conditional expectations, meaning and solution of Ito differential equations. Changes of measure on paths: Feynman--Kac formula, Cameroon--Martin formula and Girsanov's theorem. The relation between continuous and discrete models: convergence theorems and discrete approximations. Measure theory is treated intuitively, not with full mathematical rigor