401364200L Brownian Motion and Stochastic Calculus
Semester  Spring Semester 2020 
Lecturers  W. Werner 
Periodicity  yearly recurring course 
Language of instruction  English 
Courses
Number  Title  Hours  Lecturers  

401364200 V  Brownian Motion and Stochastic Calculus Lectures will be recorded and published weekly on the Videoportal (https://video.ethz.ch/lectures/dmath/2020/spring/401364200L.html)  4 hrs 
 W. Werner  
401364200 U  Brownian Motion and Stochastic Calculus Groups are selected in myStudies. See at https://metaphor.ethz.ch/x/2020/fs/401364200L/  1 hrs 
 W. Werner 
Catalogue data
Abstract  This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. 
Objective  This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. 
Lecture notes  Lecture notes will be distributed in class. 
Literature   J.F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016).  I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991).  D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005).  L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000).  D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006). 
Prerequisites / Notice  Familiarity with measuretheoretic probability as in the standard DMATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in  J. Jacod, P. Protter, Probability Essentials, Springer (2004).  R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010). 
Performance assessment
Performance assessment information (valid until the course unit is held again)  
Performance assessment as a semester course  
ECTS credits  10 credits 
Examiners  W. Werner 
Type  session examination 
Language of examination  English 
Repetition  The performance assessment is offered every session. Repetition possible without reenrolling for the course unit. 
Mode of examination  oral 20 minutes 
Additional information on mode of examination  20 minutes preparation and 20 minutes exam (one candidate prepares during the 20 minutes oral exam of the previous candidate). 
This information can be updated until the beginning of the semester; information on the examination timetable is binding. 
Learning materials
Main link  Information 
Only public learning materials are listed. 
Groups
401364200 U  Brownian Motion and Stochastic Calculus  
Groups  G01 
 
G02 
 
G03 

Restrictions
There are no additional restrictions for the registration. 