SubjectsSubjects(version: 861)
Course, academic year 2019/2020
Continuous Martingales and Counting Processes - NMTP436
Title: Spojité martingaly a čítací procesy
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017 to 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Daniel Hlubinka, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Pre-requisite : NMSA405
XP//In complex pre-requisite: NMST531
Annotation -
Last update: T_KPMS (17.05.2013)
Continuous-time martingales. Predictability. Doob-Meyer decomposition of semimartingales. Counting processes and compensators. Predictable variation. Martingale stochastic integrals. Central limit theorem for martingale stochastic integrals.
Aim of the course -
Last update: T_KPMS (17.05.2013)

Introduction to continuous-time martingales and semimartingales. Variation of stochastic process, contruction and application of martingale stochastic integral with emphasis to survival analysis.

Course completion requirements -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (23.04.2020)

Final oral exam.

Update for the academic year 2019/2020: the oral exam may be done using on-line connection in the case of need.

Literature - Czech
Last update: T_KPMS (17.05.2013)

Fleming, T.R., Harrington, D.P.: Counting processes and survival analysis. John Wiley & Sons, Inc., New York, 1991

Steele, J.M.: Stochastic calculus and financial applications. Springer, New York, 2001

Teaching methods -
Last update: T_KPMS (16.05.2013)


Requirements to the exam -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (26.02.2018)

The final exam is oral. It consists of a few questions covering the topic of the lectures.

Syllabus -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (10.06.2015)

1. Continuous time stochastic processes, counting processes, martingales.

2. Cummulative risk function, risk intensity, independent censoring, compensator.

3. Doob-Meyer decomposition, predictability, predictable quadratic variation.

4. Stochastic integral with respect to a bounded variation martingales, predictable variation and covariation of stochastic integral.

5. Martingale central limit theorems, functional central limit theorem, Gaussian processes.

6. Localization and local martingales.

Entry requirements -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (10.05.2018)

Knowledge required before enrollment:

conditional probability and conditional expectation

discrete martingales

central limit theorem

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