# Lecture and Exercises: Stochastic Partial Differential Equations (WS 2016/17)

**Lecturer:** JProf. Dr. Philipp Harms

**Exercises:** Dr. Tolulope Rhoda Fadina

**Lecture:** Thursdays 12-14 in SR 404, Eckerstr. 1

**Exercises:** Wednesdays 17-19 in SR 218, Eckerstr. 1

**Intended Audience:** MSc and PhD students with the required prerequisites

**Language:** English

## Content

This lecture is an introduction in semilinear partial stochastic differential equations (SPDEs) and methods of numerical approximation. As applications we will study interest rate and limit order book models, among others.

## Prerequisites

- Stochastic calculus
- Functional analysis
- Coding in R, MATLAB, or your favorite programming language

## Literature

- Stochastic Equations in Infinite Dimensions

G. Da Prato and J. Zabczyk

Cambridge Univ. Press (2014) - Stochastic Evolution Equations

J. Van Neerven

ISEM Lecture Notes (2007/08). - Stochastic Partial Differential Equations: Analysis and Numerical Approximations

A. Jentzen

ETH Zürich Lecture Notes (2016) - A Concise Course on Stochastic Partial Differential Equations

C. Prévôt and M. Röckner

Springer Verlag (2007) - An Introduction to Stochastic PDEs

M. Hairer

University of Warwick / Courant Institute Lecture Notes (2009) - Interest Rate Models: An Infinite-Dimensional Stochastic Analysis Perspective

R. Carmona and M. R. Tehranchi

Springer Verlag (2006)

## Lecture Notes

Lecture notes (unfinished, 10 February 2017)

## Exercises

Solving 60% of the exercises and being able to present the solution at the blackboard is required for a grade or certificate of participation.

Exercise | Due Date |

Exercise 1 | October 26, 2016 |

Exercise 2 | November 2, 2016 |

Exercise 3 | November 9, 2016 |

Exercise 4 | November 16, 2016 |

Exercise 5 | November 24, 2016 |

Exercise 6 - Joint work on student projects | November 30, 2016 |

Exercise 7 - Joint work on student projects | December 7, 2016 |

Exercise 8 | December 14, 2016 |

Exercise 9 - Joint work on student projects | December 22, 2016 |

Exercise 10 - Joint work on student projects | January 11, 2017 |

Exercise 11 | January 25, 2017 |

Exercise 12 - Joint work on student projects | February 1, 2017 |

Exercise 13 - Presentation of student projects | February 8, 2017 |

## Announcements

- The first lecture is on October 20, and the first exercise class on October 26.
- Part of the exercise classes will be devoted to joint work on student projects on advanced topics.
- The exercise class on November 23 will be held in condensed form during the class on November 24.
- The exercise classes will be held at 4pm instead of 5pm from December 14.
- The lecture and exercise class of January 18-19 are shifted to the subsequent week.