# NMAK22008U Point Processes

Volume 2022/2023
Education

MSc Programme in Statistics
MSc Programme in Mathematics-Economics
MSc Programme in Actuarial Mathematics

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
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.

The courses StatMet and MStat (alternatively MatStat from previous years), Regression and Advanced Probability 1+2 are sufficient. Advanced Probability 2 can be followed at the same time.
4 hours of lectures and 2 hours of exercises each week for seven weeks
• Category
• Hours
• Lectures
• 28
• Preparation
• 104
• Theory exercises
• 14
• Exam
• 60
• Total
• 206
Oral
Individual
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
A total of 3 individual assignments. 2 minor theoretical assignments (each with weight 15%) and 1 mixed theoretical and practical assignment (weight 70%).
Marking scale