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Course, academic year 2023/2024
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Stochastic Differential Equations - NDIR041
Title: Stochastické diferenciální rovnice
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:4/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: RNDr. Jan Seidler, CSc.
Class: DS, pravděpodobnost a matematická statistika
DS, ekonometrie a operační výzkum
Classification: Mathematics > Differential Equations, Potential Theory, Probability and Statistics
Co-requisite : NSTP149
Interchangeability : NMTP543
Is co-requisite for: NSTP176
Annotation -
Last update: JSEIDLER/MFF.CUNI.CZ (15.05.2008)
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 (19.05.2008)

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

Literature - Czech
Last update: JSEIDLER/MFF.CUNI.CZ (15.05.2008)

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: G_M (28.05.2008)


Syllabus -
Last update: JSEIDLER/MFF.CUNI.CZ (15.05.2008)

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.

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