# Probability II

Dozent: Gaultier Lambert

Dear all,

I just added a first draft of the notes for the course on my webpage: http://user.math.uzh.ch/gaultier/

These notes include the review from Probability 1 and the first part of the course on conditional expectation.

Please let me know if you find some typos or inconsistencies in the notes. Thanks in advance!

Announcements

- On Monday 19.10.2020, 10:00-11:45 (in Y27H28) there will be a theoretical lecture, instead of an exercise class.
- On Tuesday 27.10.2020, 10:15-12:00 (in Y27H28) there will be an exercise class, instead of a theoretical lecture.

## Vorlesungen

Di 10.15 - 12.00
Raum: Y27H28 Plätze: 24
Do 13.00 - 14.45
Raum: Y27H46 Plätze: 20

### Lecture Streams

This lecture offers a video stream

## Übungen

Mo 10.00 - 11.45
Y27H28 Plätze: 24
Exercises Probability II
Tutor: Gabriele Visentin

Hello all,

This is the first announcement about the plan for the course Probability II. The goal is to study (discrete) stochastic process, that is a sequence of random variables defined on a common probability space. For concreteness, I will focus on real-valued random variables and I plan to discuss several applications during the lectures and exercise sessions.

There will be three main topics:
1- Conditional expectation
2- Theory of martingales
3- Markov chains
These concepts are fundamental both in theoretical and applied probability. In particular, they have crucial applications in mathematical finance, data science and mathematical physics. From a mathematical viewpoint, this course relies on analysis, especially measure theory, but also has connections to linear algebra and combinatorics.

In the first week, I will begin this course by a review of Probability I. In the first lecture, this includes a short introduction to the foundations of probability theory, such as the key concepts of Lebesgue measure, random variables, probability law, independence, etc. I also plan to review the main modes of convergence for sequences of random variables. In the second lecture, I will review the main results from Probability I: the Borel-Cantelli Lemma, the law of large numbers and central limit Theorems. I also plan to recall the concept of characteristic functions.