### Instruction

Name | Cr | Method of study | Time | Location | Organiser |
---|---|---|---|---|---|

Probability theory II | 5 Cr | Lecture Course | 29.10.2019 - 13.12.2019 | ||

Probability theory II | 5 Cr | Lecture Course | 30.10.2018 - 14.12.2018 | ||

Probability theory II | 5 Cr | General Examination | 8.8.2018 - 8.8.2018 | ||

Probability theory II | 5 Cr | General Examination | 13.6.2018 - 13.6.2018 | ||

Probability theory II | 5 Cr | General Examination | 23.5.2018 - 23.5.2018 | ||

Probability theory II | 5 Cr | General Examination | 14.3.2018 - 14.3.2018 | ||

Probability theory II | 5 Cr | General Examination | 10.1.2018 - 10.1.2018 | ||

Probability theory II | 5 Cr | Lecture Course | 30.10.2017 - 13.12.2017 |

### Target group

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

### Prerequisites

Probability theory I and its prerequesites

### Learning outcomes

The main point is to study the principal tools in modern Probability, namely, conditional expectations and martingales, together with some examples

### Timing

Recommended time/stage of studies for completion: 1. year

Term/teaching period when the course will be offered: varying

### Contents

Discrete time Markov chains, Poisson process, conditional expectation, martingales

### Activities and teaching methods in support of learning

Lectures and exercise classes, possibly other methods like reading assignments+discussion

### Study materials

Lecture notes; D. Williams: "Probability with martingales", R. Durrett: "Probability: theory and examples"

### Assessment practices and criteria

Exam and excercises, Course will be graded with grades 1-5

### Completion methods

Exam, other methods will be described later