SubjectsSubjects(version: 978)
Course, academic year 2025/2026
   
Point Processes - NMTP564
Title: Bodové procesy
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
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
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Annotation -
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
Last update: T_KPMS (16.05.2013)
Aim of the course -

To explain mathematical foundations of stochastic geometry.

Last update: T_KPMS (16.05.2013)
Literature -

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

Last update: T_KPMS (16.05.2013)
Teaching methods -

Lecture.

Last update: T_KPMS (16.05.2013)
Syllabus -

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.

Last update: T_KPMS (16.05.2013)
 
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