SubjectsSubjects(version: 945)
Course, academic year 2023/2024
   Login via CAS
Selected topics on stochastic analysis - NSTP241
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: 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 > Probability and Statistics
Pre-requisite : NMTP543
Interchangeability : NMTP567
Annotation -
Last update: T_KPMS (10.04.2009)
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 (10.04.2009)

The goal of the course is to present some more advanced topics in stochastic analysis, related to the theory of stochastic differential equations.

Literature - Czech
Last update: T_KPMS (10.04.2009)

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: G_M (27.05.2009)


Syllabus -
Last update: T_KPMS (10.04.2009)

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

Charles University | Information system of Charles University |