MU:MU24007 Stochastic Processes - Course Information

MU24007 Stochastic Processes

Extent and Intensity

2/1/0. 5 credit(s). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Jaroslav Smítal, DrSc. (lecturer)
Mgr. Samuel Joshua Roth, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Jaroslav Smítal, DrSc.
Mathematical Institute in Opava

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)

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
  

Literature

recommended literature
• J. M. Steele. Stochastic Calculus and Financial Applications. Springer-Verlag, 2003. ISBN 0387950168. info
• G. R. Grimmett, D. Stirzaker. Probability and random processes. Oxford University Press, 2001. ISBN 0-19-857222-0. info

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 (Winter 2019, recent)
  
• Permalink: https://is.slu.cz/course/sumu/winter2019/MU24007