Submitted by bovineSurveyor on

## Category:

## Description:

The Applied Probability course deals mostly with the theory of continuous-time Markov chains, and assumes that you have already taken an undergraduate course on discrete-time Markov chains.

The course is divided into sections:

1. Basic aspects of continuous-time Markov chains

2. Qualitative properties of continuous-time Markov chains (hitting times, transience/recurrence, equilibrium distributions)

3. Queueing theory

4. Renewal theory

5. Population genetics

These cards contain definitions, statements and proofs of theorems from the course.

(The cards for renewal theory and population genetics get a little bit vague because I didn't have very long to write them. The original lecture notes are available on Dr. Sousi's course page, so see there for the full statements and proofs of the relevant theorems)

I wrote these only to aid with remembering facts for the exam - I've provided them here in the hope that they'll be helpful to someone taking an equivalent course in the same position.

They may be of interest to someone who isn't taking a course in probability, but since I've not included any of the explanation or motivation that accompanied the theorems, you'll be better off learning the material first from a textbook. I found the book by James Norris (linked to in the course page) to be very good, and it has a first chapter dealing with the discrete-time theory of Markov chains if you are unfamiliar with those too.

This may go without saying, but a fellow student has had a little trouble along these lines before: if you are taking a course in this subject, these notes are not a substitute for attending lectures.

A note on the cards: I found the LaTeX renderer used by Mnemosyne to be ugly and difficult to read, so the cards are in fact PNG images rendered from LaTeX. This does mean they are a pain to edit, and may not fit nicely on mobile screens. If anyone would like the source files to render themselves, email [email protected] and I will provide them.

## Source:

Based on my lecture notes from the Cambridge University part II course "Applied Probability", lectured in Lent term 2017 by Dr. Perla Sousi

Course page: http://www.statslab.cam.ac.uk/~ps422/ap16.html

A full typed set of the original lecture notes is available on that page, although these cards are based on what was said in lectures rather than what is written there.

## Mnemosyne Compatibility:

- 2.1+