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MU:MU24007 Stochastic Processes - Course Information

## MU24007 Stochastic Processes

**Mathematical Institute in Opava**

Winter 2021

**Extent and Intensity**- 2/1/0. 5 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Jaroslav Smítal, DrSc. (lecturer)

RNDr. Jaroslav Bradík (seminar tutor) **Guaranteed by**- prof. RNDr. Jaroslav Smítal, DrSc.

Mathematical Institute in Opava **Timetable**- Wed 9:45–11:20 5
- Timetable of Seminar Groups:

*J. Bradík* **Prerequisites**(in Czech)- TYP_STUDIA ( N )
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Applied Mathematics (programme MU, N1101)
- Mathematical Modelling (programme MU, NMgr-M)

**Course objectives**- The main goal of the course is to introduce students to the basic methods in the analysis of stochastic processes, used in mathematical models in the theory of finance. The main focus is on random walks and Wiener processes. Students successfully completing the course will be able to use these processes in mathematical modelling and techniques in their analysis.
**Syllabus**- Random walk

Reflection principle

Markovian property

Polya theorem

Arcsin laws

Discrete martingales

Filtrations

Martingale transformations

Wiener process

Cieselski's construction of Brownian motion

Continuous martingales and filtrations

- Random walk
**Literature**- G. R. Grimmett, D. Stirzaker.
*Probability and random processes*. Oxford University Press, 2001. ISBN 0-19-857222-0. info

*required literature*- J. M. Steele.
*Stochastic Calculus and Financial Applications*. Springer-Verlag, 2003. ISBN 0387950168. info

*recommended literature*- G. R. Grimmett, D. Stirzaker.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course can also be completed outside the examination period. **Teacher's information**- Obtaining the credit and passing the final oral exam.
Activity Difficulty [h] Cvičení 13 Přednáška 26 **Summary**39

- Enrolment Statistics (recent)

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