SubjectsSubjects(version: 944)
Course, academic year 2023/2024
   Login via CAS
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:
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
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)


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.

Charles University | Information system of Charles University |