Course data

Lectures: Mon 12-14 and Tue 8-10 (14.3.2011 - 2.5.2011).

Exercises: Mon 10-12 (21.3.2011 - 3.5.2011).

Instructor: Lasse Leskelä

Course data in Korppi: https://korppi.jyu.fi/kotka/r.jsp?course=100915

This course forms a continuation for the course MATS352 Stochastic differential equations 1.

Contents

• Strong and weak solution of a stochastic differential equation
• Numerical solution of a stochastic differential equation
• Markov property of a diffusion
• Generator of a diffusion and Dynkin's formula
• Applications in science, engineering, and economics

Learning outcomes

After completing the course the participant:

• Knows basic conditions for the existence of solutions to a stochastic differential equation
• Understands what is meant by uniqueness of a solution of a stochastic differential equation
• Can numerically simulate solutions of stochastic differential equations
• Recognizes when the solution of a stochastic differential equation is a diffusion
• Can compute the generator of a simple diffusion
• Knows applications of stochastic differential equations in science, engineering, and economics

Literature

During the course we shall treat Chapters 5 and 7, and selected parts of Chapters 8-11 in the book:

Language

The default language for this course is Finnish, see the Finnish course page for up-to-date information. If you wish to complete the course in English, contact the instructor.

Completion

The course is completed by passing a written exam and an assignment. The completion of the assignment is a prerequisite for attending the exam. The course grade is obtained from the formula

```  min(max(floor((x+y+z)/3 - 4), 0), 5)
```
where
```  x = points from the final exam (max 24)
y = points from the assignment (max 6)
z = points from the exercises (max 6)
```
The exercises are not compulsory, but they are warmly recommended.

The major part of the workload consists of independent study (solving the exercises, finding out how things work, etc.). Passing the course successfully requires allocating sufficient weekly time for independent study.

```Lectures             (6 x 4 h) 24 h
Exercises            (6 x 2 h) 12 h
Independent study    (6 x 8 h) 48 h
Assignment                     12 h
Preparing for the exam          8 h
Exam                            4 h
-----------------------------------
Total                         108 h
```
1 cr amounts to 27 h total work -> 4 cr equals 108 h of work.

Prerequisites

The participants are expected to master the basics of stochastic differential equations on the level of MATS352 Stokastiset differentiaaliyhtälöt 1