We will study the theory of rough paths as given in the book
P. Friz, M. Hairer,
A course on Rough Paths
Springer (2014).
This book can be downloaded free of charge from the authors' home pages.
Seminar zufällige Matrizen (Hauptesmeinar)
Ein Informationsblatt finden Sie hier.
Interacting Particle Systems (in english)
In this lecture we will study stochastic jump processes in continuous time and interacting particle systems. We will start with continuous time Markov Chains, then go on to general Feller processes. We will apply this theory to study interacting particle systems such as the Ising model, the simple exclusion process, or the voter model.
Literature:
T. Liggett:
Continuous Time Markov Processes. An Introduction
(Chapters 2,3,4).
AMS Publishing
Further reading, not much of which will be covered in the lecture:
T. Liggett:
Interacting particle systems
Springer Classics in Mathematics
C. Kipnis, C. Landim:
Scaling Limits of Interacting Particle Systems
Springer Grundlehren
More information on the TUCan website
Hauptseminar: Geometrische Aspekte Brown'scher Bewegung
Hier behandeln wir ausgewählte Kapitel aus dem Buch
P. Mörters, Y. Peres:
Brownian Motion
Cambridge University Press.
Dieses Buch ist auf der home page von Peter Mörters kostenfrei verfügbar.
Stochastische Prozesse
Inhalt der Vorlesung sind stochastische Prozesse in stetiger Zeit, mit einem Schwerpunkt auf Brown'scher Bewegung, Ito-Kalkül und stochastischen Differentialgleichungen.
Literatur:
1.
P. Mörters, Y. Peres:
Brownian Motion
Cambridge University Press.
Dieses Buch ist auf der home page von Peter Mörters kostenfrei verfügbar.
2.
T. Liggett:
Continuous Time Markov Processes. An Introduction
(Chapters 1, 5 and 6)
AMS Publishing
Nähere Informationen auf der TUCan website.
Alle Übungsblätter sind als zip-Archiv verfügbar.
Statistik für Humanwissenschaftler
Nähere Informationen auf der TUCan website.
Markovketten (Vertiefung)
Inhalt der Vorlesung sind ausgewählte Kapitel des Buches
D. Lewin, Y. Peres, E. Wilmer,
Markov Chains and mixing times
AMS publishing.
Dieses Buch ist auf der home page von David Lewin kostenfrei verfügbar.
Nähere Informationen auf der TUCan website.
Alle Übngsblätter sind als zip-Archiv verfügbar.
Seminar zufällige Matrizen (Hauptesmeinar)
Ein Informtaionsblatt finden Sie hier.
Quantum Mechanics: Basic principles and probabilistic methods
A zip-archive of the problem sheets and solutions is here:
Problem sheets
Typed lecture notes for the course:
Lecture notes
Partial differential equations in Finance
(Taught for Warwick Business School)
Recommended books and resources:
The course will, in large parts, follow closely the excellent course of
Bob Kohn, given in the Courant institute in New York in Spring 2011.
Therefore, the lecture notes to this course are a valuable reference.
They can be found here.
Further books:
P. Wilmott, S. Howison, and J. Dewynne,
The mathematics of financial derivatives: a student introduction, Cambridge Univ. Press
(This book has a relatively large overlap with the present course, but goes a bit further on
some topics).
L.C. Evans, Partial Differential Equations, AMS publishing.
The authorative textbook on PDE. Contains much much more than we will need.
Mark Joshi: The concepts and practice of Mathematical Finance, Cambridge Univ. Press
Good basic introduction to option pricing and Ito calculus. Does not cover much on PDE.
Lecture notes are here:
Complete lecture notes
Problem sheets with solutions:
zip-archive
Recommended books and resources:
The course will, in large parts, follow closely the excellent course of
Bob Kohn, given in the Courant institute in New York in Spring 2011.
Therefore, the lecture notes to this course are a valuable reference.
They can be found here.
Further books:
P. Wilmott, S. Howison, and J. Dewynne,
The mathematics of financial derivatives: a student introduction, Cambridge Univ. Press
(This book has a relatively large overlap with the present course, but goes a bit further on
some topics).
L.C. Evans, Partial Differential Equations, AMS publishing.
The authorative textbook on PDE. Contains much much more than we will need.
Mark Joshi: The concepts and practice of Mathematical Finance, Cambridge Univ. Press
Good basic introduction to option pricing and Ito calculus. Does not cover much on PDE.
Lecture notes are here:
Complete lecture notes
Problem sheets with solutions:
zip-archive
