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Stochastic Differential Equations - NMTP543

Title:	Stochastické diferenciální rovnice
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:4/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://simu0292.utia.cas.cz/seidler/teaching.html

Guarantor:	RNDr. Jan Seidler, CSc.
Class:	M Mgr. PMSE M Mgr. PMSE > Povinně volitelné
Classification:	Mathematics > Differential Equations, Potential Theory, Probability and Statistics
Pre-requisite :	{NMTP432 nebo NMFM408}
Is co-requisite for:	NMTP567
Is pre-requisite for:	NSTP241
Is interchangeable with:	NDIR041

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: T_KPMS (16.05.2013)

The lectures are devoted to fundamental theorems on existence, uniqueness and properties of strong and/or weak solutions to stochastic differential equations. Knowledge of basic results from stochastic analysis is presupposed.

Aim of the course -

Last update: T_KPMS (16.05.2013)

Students will learn basic results from the theory of stochastic differential equations.

Course completion requirements -

Last update: RNDr. Jitka Zichová, Dr. (13.05.2023)

Oral exam.

Literature - Czech

Last update: T_KPMS (16.05.2013)

Karatzas, I., Shreve, S.E.: Brownian motion and stochastic calculus. Springer Verlag, Berlin, 1988

Krylov, N.V.: Introduction to the theory of diffusion processes. American Math. Society, Providence, 1995.

Teaching methods -

Last update: T_KPMS (16.05.2013)

Lecture.

Requirements to the exam -

Last update: RNDr. Jitka Zichová, Dr. (13.05.2023)

Oral exam according to sylabus.

Syllabus -

Last update: RNDr. Jan Seidler, CSc. (27.09.2020)

1. The Burkholder-Davis-Gundy inequality.

2. Linear equations.

3. Basic results on existence and uniqueness of strong solutions to equations with Lipschitz coefficients.

4. Representation of continuous martingales by time-changes and stochastic integrals.

Entry requirements -

Last update: RNDr. Jan Seidler, CSc. (28.05.2019)

Students should be acquainted with the basics of stochastic analysis: the Wiener process, continuous-time martingales, stochastic integrals, the Itô formula.