# 401-3642-00L Brownian Motion and Stochastic Calculus

Semester | Spring Semester 2018 |

Lecturers | W. Werner |

Periodicity | yearly recurring course |

Language of instruction | English |

### 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 measure-theoretic probability as in the standard D-MATH 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 re-enrolling 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

No public learning materials available. | |

Only public learning materials are listed. |

### Courses

Number | Title | Hours | Lecturers | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

401-3642-00 V | Brownian Motion and Stochastic Calculus | 4 hrs |
| W. Werner | ||||||||||||||||||

401-3642-00 U | Brownian Motion and Stochastic Calculus Fri 8-9, Fri 9-10 or Fri 12-13 depending on sufficient demand | 1 hrs |
| W. Werner |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |