## Material

The lectures will be based on

the lecture notes of Timo Seppalainen
## Format

Schedule see Mastermath website

## Prerequisites

Basic knowledge of real analysis, probability theory. Some knowledge of functional analysis is helpful.

Recommendend books on probability theory:

David Williams, Probability with Martingales
J. Michael Steele: Stochastic Calculus and Financial Applications
Kallenberg, Foundations of Modern probability (this is quite advanced)
Recommendend books on real analysis:

Rudin, Real Analysis
Aliprantis and Burkinshaw, Principles of real analysis
Measure theory, Fremlin, Measure theory volume 1.
A nice handout on measure theory and conditional expectations by Jan van Neerven
Recommendend books on functional analysis:

Bowers and Kalton, An Introductory Course in Functional Analysis
## Coordinates

see mastermath

## Teachers

- Pranab Mandal (lectures 9-12), Mark Veraar (lectures 1-8),

Exercises till week 2
Selection of answers till week 1
## Week 1: Introduction and Conditional expectations

Read chapter 1
For selection of exercises see the above file
## Week 2: Filtrations stopping times and quadratic variation

Read sections 2.1 and 2.2 and bounded variation in chapter 1
For selection of exercises see the above file
Every measurable process which is adapted can be shown to have a version which is progressively measurable.
Details can be found in Ondrejat and Seidler.
A good explanation of Dynkin's pi-lambda lemma can be found in David Williams book. The proofs are quite short.
More information on this course will no longer be put on this website but instead on wikispaces.
Please send me an email with the request to be included if you want.