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Stochastic processes

Code: 92983
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Zoran Vondraček - Lectures
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: To introduce basic types of random processes in continuous time and explain fundamental results for such processes.

COURSE DESCRIPTION AND SYLLABUS:
1. Markov chains in continuous time. Definition and construction. Markov property. Backward equation, generating matrix. Poisson process. Stationary and limiting distribution. Laplace transformation method.
2. Renewal theory. Analytical background. Renewal counting. Renewal equation. Limiting renewal theorems. Poisson process as a renewal process.
3. Introduction to Brownian motion. Definition and random walks. Basic properties of Brownian motion. Markov property and strong Markov property. Stopping times of Brownian motion and realtionship with martingales.
Literature:
  1. S. I. Resnick: Adventures in Stochastic Processes
  2. P. Bremaud: Markov Chains: Gibbs fields, Monte Carlo simulations and queues, 2nd edition
  3. G. R. Grimmett, D. R. Stirzaker: Probability and Random Processes
  4. J. R. Norris: Markov Chains
Prerequisit for:
Enrollment :
Passed : Markov chains
2. semester
Mandatory course - Regular study - Financial and Business Mathematics
Consultations schedule: