Stochastic Processes II (FS 2018)

Lecturer

Assistant

  • Dr. Florian Wespi

Date and Venue

  • Wednesday, 16 - 18 h, B77 (ExWi)
  • Friday, 10 - 12 h, B78 (ExWi)
  • Start: Wednesday, February 21, 2018

 

Further information and assignmnets can be found at the Ilias webpage

Scope and contents

This lecture introduces the theory of stochastic processes with continuous time

1 Some mathematical notions

1.1 Measurable spaces

1.2 Probability spaces

1.3 Random elements

1.4 Finite dimensional distributions of stochastic processes

1.5 Sample path regularity

1.6 Filtration and stopping time 

2 Wiener process and Ito integral

2.1 The Wiener process, self-similarity and variation

2.2 Extrema and hitting times of the Wiener process

2.3 Ito integral

2.4 Ito process and stochastic differential equations

3 Levy processes

3.1 Infinite divisibility

3.2 Levy processes and examples

3.3 Subordinators

3.4 Martingales and stopping times

3.5 Jumps and Poisson random measure