Stochastic Processes II (FS 2018)

Lecturer

  • Prof. Dr. Riccardo Gatto, gatto@stat.unibe.ch, 031 631 8807
  • Office hour: upon appointment, office 010, Alpeneggstrasse 22

Assistant

  • Dr. Florian Wespi

Date and Venue

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

Other information

6 ECTS credit points

Administrative information (Gefässe/blocks, registration to exam): KSL

Prerequisites

  1. "Wahrscheinlichkeitstheorie" or equivalent course on probability theory with measure theory. The exam must be already passed with success. The teacher must be consulted for the determination of the equivalence.
  2. At least "Analysis I" and "Analysis II" or equivalent courses. The exams must be already passed with success. The teacher must be consulted for the determination of the equivalence.

Exam

  1. Oral examination of 25-30 minutes 
  2. Conditions for enrollement to exam: hand over of 2/3 of assignment solutions

Scope and contents

This lecture introduces the theory of stochastic processes with continuous time

1 Probability spaces and random elements

1.1 Measurable spaces

1.2 Probability spaces

1.3 Random elements

1.4 Finite dimensional distributions of stochastic processes

2 Ito processes 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 processes 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