 Continuous time stochastic Processes:
Examples, Filtrations, Stopping times, Brownian
motion, Poisson process
 Martingales:
Optional sampling theorem and Doob's inequalities, Quadratic variation
and covariaton, Martingale convergence theorem
 Stochastic Integrals:
Definition, Change of time variable, Change of Integrator, Ito's
formula
 Stochastic Differential Equations:
Examples, Uniqueness of solutions of SDEs, Gronwall inequality for SDEs, Existence of
solutions, Moment estimates
 Diffusions:
Generator for a diffusion process, Exit distributions in
one dimension, Dirichlet problems, Harmonic functions, Parabolic equations
 Properties of paths:
Equations for probability distributions, Stationary distributions, Long term
behaviour
 Poisson random measure:
Integration w.r.t. a Poisson random measure, Centered Poisson
random measure, SDEs driven by Poisson measures
