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Course, academic year 2019/2020
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Stochastic Differential Equations - NMTP543
Title in English: Stochastické diferenciální rovnice
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:4/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
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
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 - Czech
Last update: RNDr. Jitka Zichová, Dr. (19.04.2018)

Složení ústní zkoušky.

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 - Czech
Last update: RNDr. Jan Seidler, CSc. (11.10.2017)

Zkouška je ústní, požadavky odpovídají sylabu předmětu v rozsahu, který byl presentován na přednášce.

Syllabus -
Last update: T_KPMS (16.05.2013)

1. The Burkholder-Davis-Gundy inequality.

2. Basic results on existence and uniqueness of strong solutions to equations with Lipschitz or locally Lipschitz coefficients. Khas'minskii's

test for nonexplosions.

3. Linear equations.

4. Markovianity of solutions.

5. Representation of continuous martingales by stochastic integrals.

6. Exponential martingales nad Novikov's condition.

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.

 
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