### Instruction

Name Cr Method of study Time Location Organiser
Stochastic Methods 10 Cr General Examination 17.4.2020 - 17.4.2020
Stochastic Methods 10 Cr General Examination 5.6.2020 - 5.6.2020
Name Cr Method of study Time Location Organiser
Stochastic Methods 10 Cr General Examination 13.12.2019 - 13.12.2019
Stochastic Methods 10 Cr Lecture Course 3.9.2019 - 16.12.2019
Stochastic Methods 10 Cr Lecture Course 10.9.2018 - 11.12.2018
Stochastic Methods 10 Cr General Examination 18.5.2018 - 18.5.2018
Stochastic Methods 10 Cr General Examination 16.2.2018 - 16.2.2018
Stochastic Methods 10 Cr Lecture Course 5.9.2017 - 21.12.2017

### Target group

Master’s Programme in Theoretical and Computational Methods is responsible for the course.

Module where the course belongs to:

• TCM300 Advanced Studies in Theoretical and Computational Methods

The course is available to students from other degree programmes.

### Prerequisites

• Differential and integral calculus, linear algebra, complex numbers, (ordinary and partial) differential equations.
• Elementary probability (either Todennäköisyyslaskenta I and/or II or similar knowledge, possibly from Fysiikan Matemaattiset Menetelmät IIa/b).

### Learning outcomes

• You will learn to know the essential theories and methods of stochastics as well as stochastic models frequently encountered in applications.
• You will understand how to treat mathematically random phenomena and related models.
• If the implementation of the course emphasises more computational methods, you’ll learn to them also in practise in small tasks and/or a project work.

### Timing

Can be taken in the early or later stages of studies. This can even be the only stochastics course you study.

Lectured every second year.

### Contents

• The course covers essential (theoretical and/or computational) methods in stochastics and emphasises their applications to natural sciences (and possibly also to other fields, e.g. finance and insurance mathematics). Although the topics may vary between years, we aim to cover the essential parts of background in the probability theory and topics in stochastic processes (e.g. Markov chains, random walks, Brownian motion, Poisson process) and stochastic calculus (integration with respect to random processes, Ito’s formula etc.).
• The course is aimed to be self-contained for those students that are more interested in the applications. The course can be complementary to the other courses in stochastics (for those students that have studied or plan to study more stochastics courses) in that it emphasises more the applications.

### Activities and teaching methods in support of learning

Weekly lectures and exercises. Other teaching activities will be announced at the beginning of the course.

### Assessment practices and criteria

The course is graded based on the exam, exercises and the other compulsory course work announced at the beginning of the course.

### Recommended optional studies

• Courses in stochastics (Probability theory, Stochastic analysis etc.)
• Courses in mathematical physics

### Completion methods

Exam and exercises.