Login for PhD students/staff at UCPH      Login for others
Point Processes
Provider: Faculty of Science

Activity no.: 7010-22-07-31 
Enrollment deadline: 21/11/2022
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time21.11.2022, at: 08:00 - 27.01.2023, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserNiels Richard Hansen    E-mail address: niels.r.hansen@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 2
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam formContinuous assessment
Exam detailsA total of 3 individual assignments. 2 minor theoretical assignments (each with weight 15%) and 1 mixed theoretical and practical assignment (weight 70%).
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Lectures28.00
Preparation104.00
Theory exercises14.00
Exam60.00
Sum206.00
Content
- Random measures and Poisson processes.
- Stochastic processes with locally bounded variation.
- Integration w.r.t. random measures and locally bounded variation processes.
- Stochastic integral equations, numerical solutions and simulation algorithms.
- Elements of continuous time martingale theory.
- Change of measure, the likelihood process and statistical inference.
- Multivariate asynchronous event time models.

Learning outcome
Knowledge:
- Aspects of stochastic analysis for processes with finite local variation.
- Statistical methods for estimation and model selection.
- Applications of concrete multivariate recurrent event time models.

Skills: Ability to
- compute with stochastic integrals w.r.t. locally bounded variation processes
- construct univariate and multivariate models as solutions to stochastic integral equations
- simulate solutions to stochastic integral equations
- estimate parameters via likelihood and penalized likelihood methods
- implement the necessary computations
- build dynamic models of multivariate event times, fit the models to data, simulate from the models and validate the models.

Competences: Ability to
- analyze mathematical models of events with appropriate probabilistic techniques
- develop statistical tools based on the mathematical theory of event times
- assess which asynchronous event time models are appropriate for a particular data modelling task

Teaching and learning methods
4 hours of lectures and 2 hours of exercises each week for seven weeks

Remarks
Recommended Academic Qualifications:
Probability theory and mathematical statistics on a measure theoretic level. Knowledge of stochastic process theory including discrete time martingales and preferably aspects of continuous time stochastic processes.

Search
Click the search button to search Courses.


Course calendar
See which courses you can attend and when
JanFebMarApr
MayJunJulAug
SepOctNovDec



Publication of new courses
All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.