1. SylabUZ
2. Faculty of Physics and Astronomy
3. winter term 2018/2019
4. Physics and Astronom - PhD studies
5. Lecture III-P

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Lecture III-P - course description

Aim of the course

Mathematical foundations of stochastic processes and numerical methods for their modeling.
After the course, knowledge of both theory and its practical application at the level enabling independent scientific work is expected.

Prerequisites

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Knowledge of mathematical analysis, basics of physics, probability theory, programming skills.

Scope

1. Introduction to the Langevin equation and Brownian motion
2. Wiener processes
3. Stochastic integral calculus (Ito integral and Stratonovich integral)
4. Applications of Wiener processes (modeling of diffusion and chemical reactions)
5. alfa-stable processes and their applications

Teaching methods

Lecture with the use of multimedia.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

The exam is in a written form. The students receive a problem task, in which they must choose the right method of data analysis and must interpret the results obtained.

Recommended reading

[1] N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland Personal Library 1992

[2] C.W. Gardiner, Handbook of stochastic methods fo Physics, Chemistry and the Natural Sciences, Springer-Verlag 1983

[3] A. Janicki, A. Weron, Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes, Marcel Dekker. Inc. 1994

[4] A. Weron, R. Weron, Computer Simulation of Levy \alpha-Stable Variables and Processes, Lecture Notes in Physics 457, 379-392, Springer-Verlag 1995

Further reading

[1] Z. Schuss, Teoria i zastosowania stochastycznych równań całkowych, PWN, Warszawa 1989

Notes

Modified by dr Joanna Kalaga (last modification: 30-08-2018 10:38)