Stochastic Modelling

Facts  
Duration: 1 semester
Period: Fall Semester
Credits: 6 ECTS
Contact Hours: 64
Self-study: 152
Hours: 216

Main Objectives

1. The studying of the modern stochastic calculus and its application to the modeling of stochastic dynamical systems described by stochastic differential and stochastic difference equations.

2. Application of the theory of measurable maps, measure theory and methods of analytic functions for the development of the basic concepts of the modern theory stochastic processes such as

  • conditional expectations and their applications in the theory of stochastic processes;
  • stochastic basis and basic measurable structure;
  • Markov moments;
  • random sets;
  • andom processes;
  • martingales;
  • Stochastic integration.

Learning Outcomes

In mastering the subject the student will acquire the following knowledge:

the basic principles of modern stochastic calculus.

To be able: to properly use the stochastic integration methods, perform correct limit transitions in the localization methods of stochastic processes by the stopping times.

To have: the skills to the limiting transitions under the sign o fconditional expectations, the stopping times tool, the stochastic integration methods.

Professor

Serguei Pergamenchtchikov, Doctor of Science

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Course unit code

Б.2.2

Course unit title

Basic course

Name(s), surname(s) and title of lecturer(s)

Serguei Pergamenchtchikov, Doctor of Science, Professor

Semester

1

ECTS credits

6

Working hours

Contact hours

lectures

32

seminars

32

Self-study

152

Total

216

Work placement

Laboratory works in Computer class

Prerequisites

To study the course one needs «Topology", "Mathematical Analysis", "Functional Analysis", "Theory of functions of a complex variable" and "Theory of Probability and Mathematical Statistics".

Language of instruction

English (Russian)

Objectives of the course

Learning outcomes

A student’s assessments methods

1.1. The studying of the modern stochastic calculus and its application to the modeling of stochastic dynamical systems described by stochastic differential and stochastic difference equations.

1.2. Application of the theory of measurable maps, measure theory and methods of analytic functions for the development of the basic concepts of the modern theory stochastic processes such as

- conditional expectations and their applications in the theory of stochastic processes;

- stochastic basis and basic measurable structure;

- Markov moments;

- random sets;

- random processes;

- martingales;

- Stochastic integration.

In mastering the subject the student will acquire the following knowledge:

the basic principles of modern stochastic calculus.

To be able: to properly use the stochastic integration methods, perform correct limit transitions in the localization methods of stochastic processes by the stopping times.

To have: the skills to the limiting transitions under the sign of conditional expectations, the stopping times tool, the stochastic integration methods.

The current control of mastering the discipline includes two written test.

The final control – exam.

Teaching methods

Lectures, Labs

List of Topics

Topic title

Contact hours

Assignments and independent study hours

Conditional expectations

8

Stopping times

8

Random sets

8

Random processes

10

Written test 1

Optional and predictable processes

8

Martingales

10

Stochastic integral

12

Written test 2

64

Exam

Assessment requirements

In during the semester 40 points

Assessment criteria

Each test 20 points

The composition of final accumulative mark

Exam 60 points.

Examination ticket consists of two theoretical questions (10x2=20) and two exercises (20x2=40).

Author of the course

Serguei Pergamenchtchikov