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Course, academic year 2023/2024
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Selected Topics on Stochastic Analysis - NMTP567
Title: Vybrané partie ze stochastické analýzy
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, 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:
Guarantor: RNDr. Jan Seidler, CSc.
Class: M Mgr. PMSE
M Mgr. PMSE > Volitelné
Classification: Mathematics > Probability and Statistics
Co-requisite : NMTP543
Is interchangeable with: NSTP241
Annotation -
Last update: T_KPMS (16.05.2013)
The course focuses on two topics: a) weak solutions to stochastic differential equations (existence of solutions to equations with a bounded Borel drift, subjected to an additive noise, and to equations with continuous coefficents, uniqueness of solutions in law and pathwise), b) qualitative properties of solutions (various types of Lyapunov stability).
Aim of the course -
Last update: T_KPMS (16.05.2013)

The goal of the course is to present some more advanced topics in stochastic analysis, related to 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)

I. Karatzas, S. Shreve: Brownian motion and stochastic calculus, Springer, New York 1991

D. W. Stroock: Lectures on stochastic analysis: Diffusion theory, Cambridge Univ. Press, Cambridge 1987

Teaching methods -
Last update: T_KPMS (16.05.2013)


Requirements to the exam -
Last update: RNDr. Jitka Zichová, Dr. (13.05.2023)

Oral exam according to sylabus.

Syllabus -
Last update: T_KPMS (16.05.2013)

1. Girsanov's theorem and equations with a bounded Borel drift

2. Weak solutions to equations with continuous coefficients

3. Uniqueness of solutions and the Yamada-Watanabe theory

4. Stability of solutions in quadratic mean, in probability, and almost surely

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

A sound knowledge of basic theory of stochastic differential equations is assumed.

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