MUNAM3 Applied Statistics and Probability

Mathematical Institute in Opava
Summer 2013
Extent and Intensity
0/0. 0 credit(s). Type of Completion: -.
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
To verify whether the student has successfully mastered the studied subject and gained knowledge and skills needed for either further study or practice.
Syllabus (in Czech)
  • Aplikovaná statistika a pravděpodobnost
    Míra, integrál a pravděpodobnost:
    - Základní vlastnosti míry, Carathéodoryho věta.
    - Hausdorffova, Lebesgueova-Stieltjesova a Lebesgueova míra.
    - Měřitelné funkce, Lebesgueův integrál.
    - Pravděpodobnostní prostor, náhodné veličiny, náhodné procesy, Markovovy řetězce.
    Základní metody finanční matematiky:
    - Náhodné procházky a Polyova věta, generující funkce a diskrétní martingály, Wienerův proces a spojité martingály.
    - Stochastický integrál, Itóovo lemma.
    - Black-Scholesův model - odvození, řešení, aplikace.
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 Winter 2010, Summer 2011, Winter 2011, Summer 2012, Winter 2012, Winter 2013, Summer 2014, Winter 2014, Summer 2015, Winter 2015, Summer 2016, Winter 2016, Summer 2017, Winter 2017, Summer 2018, Winter 2018, Summer 2019.
  • Enrolment Statistics (Summer 2013, recent)
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