SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Advanced Theory of Stochastic Differential Equations - NMTP604
Title in English: Pokročilé partie stochastických diferenciálních rovnic
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Note: you can enroll for the course repeatedly
Guarantor: prof. RNDr. Bohdan Maslowski, DrSc.
Class: Pravděp. a statistika, ekonometrie a fin. mat.
Annotation -
Last update: T_KPMS (01.06.2016)
The subject aims at extending the knowledge of students so that they would be able to work independently on the field of stochastic differential equations. The emphasis is put on the presentation of the theory of stochastic evolution equations, in particular, on the semigroup approach to stochastic differential equations in Hilbert spaces and differences between this theory and the classical approach to (finite-dimensional) stochastic differential equations. For PhD students.
Aim of the course -
Last update: T_KPMS (06.05.2014)

Students will get acquainted with basics of the theory of stochastic evolution equations. As the basic method stochastic analysis in infinite dimensional state spaces is used.

Course completion requirements - Czech
Last update: RNDr. Jitka Zichová, Dr. (25.04.2018)

Složení ústní zkoušky.

Literature - Czech
Last update: T_KPMS (06.05.2014)

1. G. Da Prato, J. Zabczyk: Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, Cambridge, 1992 (1. Edition)

2. A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983 (1. Edition)

3. I. Karatzas, S.E.Shreve: Brownian Motion and Stochastic Calculus, Springer-Verlag, 1988 (1. Edition)

Teaching methods -
Last update: T_KPMS (06.05.2014)

Lecture.

Requirements to the exam - Czech
Last update: prof. RNDr. Bohdan Maslowski, DrSc. (09.10.2017)

Zkouška je ústní a jejím předmětem budou vybrané kapitoly z teorie stochastických diferenciálních rovnic a stochastických evolučních rovnic v rozsahu dohodnutém v daném roce studia.

Syllabus -
Last update: T_KPMS (01.06.2016)

1. Cylindrical H-valued Brownian motion, cylindrical measures, Gaussian measures in Hilbert spaces

2. Strongly continuous semigroups

3. Stochastic integral in Hilbert spaces

4. Stochastic convolution integrals and linear equations in Hilbert spaces

5. Semilinear SEEs and some remarks on large time behaviour od solutions

 
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