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Course, academic year 2019/2020
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Point Processes - NMTP564
Title in English: Bodové procesy
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2014
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: not taught
Language: Czech, English
Teaching methods: full-time
Guarantor: prof. RNDr. Jan Rataj, CSc.
Class: M Mgr. PMSE
M Mgr. PMSE > Volitelné
Classification: Mathematics > Probability and Statistics, Topology and Category
Incompatibility : NMAT011
Annotation -
Last update: T_KPMS (16.05.2013)
Random measures on locally compact spaces, point processes as integer-valued random measures, existence and uniqueness results, Poisson processes, moment measures and the Laplace functional, Palm distribution, convergence of point processes, stationary point processes in $R^d$, point processes on the set of compact subsets of $R^d$, the Boolean model, exterior conditioning. Literature: (1) D.J.Daley, D.Vere-Jones: An Introduction to the Theory of Point Processes (Springer, 1988) (2) O.Kallenberg: Random Measures (Akademie-Verlag Berlin, 1983) (3) D.Stoyan, W.S.Kendall, J.Mecke: Stocha
Aim of the course -
Last update: T_KPMS (16.05.2013)

To explain mathematical foundations of stochastic geometry.

Literature -
Last update: T_KPMS (16.05.2013)

Literature:

(1) D.J.Daley, D.Vere-Jones: An Introduction to the Theory of Point Processes

(Springer, 1988)

(2) O.Kallenberg: Random Measures (Akademie-Verlag Berlin, 1983)

(3) D.Stoyan, W.S.Kendall, J.Mecke: Stocha

Teaching methods -
Last update: T_KPMS (16.05.2013)

Lecture.

Syllabus -
Last update: T_KPMS (16.05.2013)

1. Random measures and point processes on locally compact spaces. 2. Existence of processes with given finite dimensional distributions. 3. Intensity measure, moment measures, Laplace functional. 4. Palm distribution of a point process. 5. Poisson point process and Boolean model. 6. Weak convergence of point processes. 7. Gibbs point processes.

 
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