MU24007 Stochastic Processes

Mathematical Institute in Opava
Winter 2015
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Samuel Joshua Roth, Ph.D. (lecturer)
Mgr. Zuzana Roth, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jaroslav Smítal, DrSc.
Mathematical Institute in Opava
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
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
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2010, Summer 2011, Summer 2012, Winter 2012, Winter 2013, Winter 2014, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2021, Winter 2022, Winter 2023.
  • Enrolment Statistics (Winter 2015, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2015/MU24007