# NMAK22008U Point Processes

Volume 2024/2025
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 and the likelihood process.
• Statistical inference based on martingale estimating equations.
Learning Outcome

Knowledge:

• Poisson random measures.
• Aspects of stochastic analysis for processes with finite local variation.
• Statistical methods for estimation and model selection.
• Examples of 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 other martingale estimating equations
• 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 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, MStat, Probability Theory 2 and Regression are sufficient. Stochastic Processes in Continuous Time and/or Brownian Motion are also recommended but not necessary.
4 hours of lectures and 2 hours of exercises each week for seven weeks
• Category
• Hours
• Lectures
• 28
• Preparation
• 163
• Theory exercises
• 14
• Exam
• 1
• Total
• 206
Written
Oral
Individual
Continuous feedback during the course of the semester

There will be written and oral feedback for all three group assignments, which will be given to the group.

There will be continuous oral and individual feedback during the exercise classes.

Credit
7,5 ECTS
Type of assessment
Oral exam on basis of previous submission, 20 minutes (no preparation time)
Type of assessment details
A total of 3 group assignments consisting of a mix of theory and practice are to be handed in during the course.

The three approved assignments form the basis for a final 20 minutes individual oral exam without preparation.
Aid
All aids allowed
Marking scale