The aim of the mini course is to give a self-consistent introduction into the basic theory about Stochastic Differential Equations (SDE) driven by the Brownian motion. The following topics are planed:
(a) Brownian motion
(b) Stochastic integration (Itô integral) with respect to the Brownian motion
(c) Ito’s formula
(d) Existence and uniqueness of solutions to SDEs under Lipschitz conditions
(e) Feynman-Kac theory for parabolic PDEs
(f) A remark on weak solutions and SDEs under non-Lipschitz conditions