Stochastic analysis deals with stochastic processes in continuous time. In this course we will cover, among other things, the following topics:

Gaussian processes; construction and properties of Brownian motion; filtrations and stopping times; continuous-time martingales; continuous semimartingales; quadratic variation; stochastic integration; Ito formula; Girsanov's theorem and change of measures; time reparameterization; martingale representation; stochastic differential equations and diffusion processes; connection to partial differential equations.

More information can be found at the Homepage of the course 19208001 Stochastik III.

Time and place

Lectures: Wednesdays, 08:30-10:00, SR 046, Takustr. 9, and 
                Thursdays, 10:15-11:45, SR 046, Takustr. 9.

Exercise Sessions: Thursdays, 16:00-17:30, SR 032, Arnimallee 6.

Office time: please write me an email ( lgaleati@zedat.fu-berlin.de ) to fix an appointment.

Requirements

Prerequisites are Analysis I-III and Stochastics I and II. Functional analysis is helpful but not required.

Assessment

To receive credits fo the course you need to:

• actively participate in the exercise sessions 
• work on and successfully solve the weekly homework exercises (you need at least 50% of the points, on average, to pass)
• pass the final exam which will be an oral examination

Exam

The final exam will be oral, one student at a time, and will take place in my office (Office 205, Arnimallee 7). For this reason, it might take place on multiple dates of the same week. Current candidate dates for the exam are

- Wednesday 19^th February 2025;

- Thursday, 20^th February 2025;

- Friday, 21^st February 2025.

Exact times will be communicated later on.

Exercises 

Problem sheets will be put online every Wednesday and can be found under Assignements in the MyCampus/Whiteboard portal. Solutions (in pairs!) are due on Wednesday of the following week - please submit them physically on Wednesday during the 08:30-10:00 lecture. The solutions can be either hand-written, or typed in latex, or any other solution that suits you, but I still want to receive a physical copy in order to correct it.

Materials and references

Lecture notes will be made available on Whiteboard and updated as the course goes on. Many additional references are mentioned therein as well as at the Homepage of the course. As a main reference for the course apart from the lecture notes, see:

• Jean-François Le Gall: Brownian motion, martingales, and stochastic calculus. Springer, 2016.