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Probability and Stochastic Analysis - NSTP153

Title:	Pravděpodobnost a stochastická analýza
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
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:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	NMTP432

Guarantor:	doc. RNDr. Daniel Hlubinka, Ph.D.
Class:	DS, pravděpodobnost a matematická statistika DS, ekonometrie a operační výzkum
Classification:	Mathematics > Probability and Statistics
Incompatibility :	NMTP432, NSTP149
Interchangeability :	NMTP432, NSTP149

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Annotation -

Last update: T_KPMS (14.05.2003)

Discrete and continuous martingales, introduction to stochastic integration, applications. A course for PhD students.

Aim of the course -

Last update: T_KPMS (23.05.2008)

An advanced lecture on Brownian motion and stochastic integral is designed to to complete a student knowledge and abilities to handle a stochastic process both from theoretical and applied view.

Literature - Czech

Last update: G_M (25.05.2010)

Dupačová, J., Hurt, J., Štěpán, J.: Stochastic Modeling in Economics and Finance.

Kluwer Academic Publishers, London, 2002.

O. Kallenberg: Foundations of modern probability. Springer, New York, 2002.

I. Karatzas, D.E. Shreve: Brownian motion and stochastic calculus. Springer, New York, 1991.

Teaching methods -

Last update: G_M (28.05.2008)

Lecture.

Syllabus -

Last update: G_M (25.05.2010)

1. Stochastic processes and their construction.

2. Continuous martingales and Brownian motion.

3. Markov times, martingales stopped by a Markov time.

4. Spaces of stochastic processes.

5. Doob Meyer decomposition. Quadratic variation of a continuous martingale.

6. Stochastic integral and its properties.

7. Exponential martingales and Lévy characterization of Brownian motion.

8. Trend removing Girsanov theorem for Brownian motion.

9. Brownian representation of a continuous martingale by a stochastic integral.

10. Local time of a continuous martingale.

11. An introduction to the theory of stochastic differential equations.

12. Stochastic analysis applied to physics and financial mathematics.