Hand-written lecture notes:

Part 1 (conditional expectations, discrete-time martingales)

Part 2 (stochastic processes, Brownian motion, Markov chains)

These notes are mainly based on Le Gall's notes and Klenke's book. Thanks to Martin Slowik for useful discussions.

Exercises:

• Sheet 1

• Sheet 2

• Sheet 3

• Sheet 4

• Sheet 5

• Sheet 6

• Sheet 7

• Sheet 8

• Sheet 9

• Sheet 10

• Sheet 11

• Sheet 12

• Sheet 13

The official website for this course is here.