Professur für Wahrscheinlichkeitstheorie

Wintersemester / winter term 2019/20

Malliavin Calculus

Modul Ma-MMMA (Ma-MMMA)

Umfang / contact: 4+0
Ort / venue: Willersbau, Zellescher Weg 12 -14
Zeit / time: Mo / Mon 3. DS (11:10-12:40)    WIL C204
Mi / Wed 3. DS (11:10-12:40)    WIL C204
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:
Venue:
Registration: with Ms. Schreiter (exam office)
Exam language: English (oder, auf Wunsch, Deutsch)
Prüfungsamt Aktuelles 


  • Malliavin Calculus is also known as stochastic calculus of variations. We develop a differential calculus on Wiener space (which is defined by the paths of a Brownian motion) which will allow us, e.g., to calculate the densities of a stochastic differential equation driven by a Brownian motion. In some sense, this course continuous the course on stochastic calculus, but it is not a prerequisite.
  • Prerequisites: measure-theoretic probability theory (e.g. as tought in our BSc course STOCH), martingales in continuous time (e.g. as tought in the MSc course PWM) and stochastic (Itô) integration w.r.t. a Brownian motion (e.g. as tought in the MSc course stochastic calculus)
    • Literature: A good backup reading (Brownian motion, stochastic calculus) is my own book
      • Schilling & Partzsch: Brownian Motion. An introduction to the theory of stochastic processes. De Gruyter, Berlin 2014 (2nd edn). ISBN: 978-3-11-030729-0
    • Further Literature:
      1. Ikeda & Watanabe: Stochastic Differential Equations and Diffusion Processes. North-Holland 1989 (2nd edn). ISBN: 978-1-493-30721-0
      2. Nualart: The Malliavin Calculus and Related Topics. Springer 2005. ISBN: 3-540-28328-5
      3. Watanabe: Stochastic Differential Equations and Malliavin Calculus. Springer 1984. ISBN: 3-540-12897-2
       

Stand:
Autor: René Schilling