1. komponenta

Lecture type	Total
Lectures	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE OBJECTIVES:
To acquire basic knowledge of the most important types of stochastic processes, to learn their properties and to be introduced to some simple modelling techniques in stochastic environment.

COURSE CONTENT:
1. Introduction. Conditional Expectations. Stochastic Processes, Discrete vs Continuous. Filtrations. Stopping Times. Sample Paths.
2. Poisson Process. Random Walk. Markov Chains. Transition Matrix. Invariant Measures. Examples and Applications.
3. Discrete Time Martingales. Optional Stopping Theorem. Limit Theorems. Examples and Applications.
4. Brownian Motion. Levy Processes. Martingale Characterizations. Continuous and Cadlag Processes. Examples and Applications.
5. General Markov Processes. Introduction to Semigroups. Feller Processes. Examples and Applications.

1. Diffusions, Markov Processes and Martingales, L.C.G.Rogers, D.Williams, Cambridge University Press, 2000.
2. Adventures in Stochastic Processes, S.I.Resnick, Birkhauser, 2002.
3. An Introduction to Stochastic Processes with Applications to Biology, 2nd ed, L.J.S.Allen, CRC, 2010.
4. Introduction to Stochastic Processes, 2nd ed, G.F.Lawler, Chapman and Hall/CRC, 2018.
5. Essentials of Stochastic Processes, 3rd ed, R.Durrett, Springer, 2016.
6. Applications of Stochastic Processes in Biology and Medicine, (special issue) International Journal of Stochastic Analysis, Volume 2013.

Elective courses 1, 2 - Regular study - Biomedical Mathematics

Elective courses 1, 2 - Regular study - Biomedical Mathematics