Professur für Wahrscheinlichkeitstheorie

wintersemester/winter term 2017/18

Probability with martingales

Modul "Wahrscheinlichkeitstheorie mit Martingalen" (Ma-WTHM)

Umfang / contact: 4+0
Ort / venue: Willersbau, Zellescher Weg 12 -14
Zeit / time: Di / Tue 5. DS (14:50-16:20) , WIL C 204
Do / Thu 2. DS (9:20-10:50) , WIL C 204
Übungen / tutorials: während der VL / part of the lecture
Beginn / begin: 1 Semesterwoche / 1st week of term
Niveau / level : Master / MSc
Unterrichtssprache /
language:
english
Prüfung / exam: oral exam (group examination, group size = 1, duration approx. 20 min)
Time: Tue 6/February/2018
Venue: WIL B 319, from 09:00
Registration: with Ms. Schreiter (exam office)
Exam language: either English (oder, auf Wunsch, Deutsch)
Prüfungsamt Aktuelles 


  • In this course you will get an introduction to stochastic processes in continuous time. We begin with continuous-time martingales and thir applications to path regularizations of stochastic processes. Then we will look into the problem how to construct and characterize general stochastic processes (Kolmogorov's existence theorem) which will will then apply to construct and study several continuous-time processes.
  • This lecture is the basis for further studies in the direction of stochastic analysis and advanced mathematical finance. I will continue these lectures in the winter term with a course on "Stochastic Calculus" and a seminar or a lecture on selected topics in stochastic processes (e.g. jump processes) in the following winter term.
  • Prerequisites: measure-theoretic probability theory (e.g. as tought in our BSc course STOCH) and basic knowledge of discrete-time martingales (e.g. as tought in the BSc course STOCHV).
    • Literature: I will not follow any particular text, but the following books contain (more than) the material covered in this lecture course:
      1. Ikeda & Watanabe: Stochastic Differential Equations and Diffusion Processes. North-Holland 1989 (2nd edn). ISBN: 978-1493307210
      2. Revuz & Yor: Continuous Martingales and Brownian Motion. Springer, Berlin 2005 (3rd edn). ISBN: 978-3540643258
      3. Rogers & Williams: Diffusions, Markov Processes and Martingales. Vol. 1. Cambridge University Press, Cambridge 2000 (2nd edn). ISBN 978-0521775946
      4. Schilling & Partzsch: Brownian Motion. An introduction to the theory of stochastic processes. De Gruyter, Berlin 2014 (2nd edn). ISBN: 978-3-11-030729-0
       

Stand:
Autor: René Schilling