Arnulf Jentzen: Catalogue data in Autumn Semester 2016 |
| Name | Dr. Arnulf Jentzen |
| Field | Applied Mathematics |
| URL | http://www.sam.math.ethz.ch/~jentzena |
| Department | Mathematics |
| Relationship | Assistant Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-4475-66L | Partial Differential Equations and Semigroups of Bounded Linear Operators  | 4 credits | 2G | A. Jentzen | |
| Abstract | In this course we study the concept of a semigroup of bounded linear operators and we use this concept to investigate existence, uniqueness, and regularity properties of solutions of partial differential equations (PDEs) of the evolutionary type. | ||||
| Learning objective | The aim of this course is to teach the students a decent knowledge (i) on semigroups of bounded linear operators, (ii) on solutions of partial differential equations (PDEs) of the evolutionary type, and (iii) on the analytic concepts used to formulate and study such semigroups and such PDEs. | ||||
| Content | The course includes content (i) on semigroups of bounded linear operators, (ii) on solutions of partial differential equations (PDEs) of the evolutionary type, and (iii) on the analytic concepts used to formulate and study such semigroups and such PDEs. Key example PDEs that are treated in this course are heat and wave equations. | ||||
| Lecture notes | Lecture Notes are available in the lecture homepage (please follow the link in the Learning materials section). | ||||
| Literature | 1. Amnon Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York (1983). 2. Klaus-Jochen Engel and Rainer Nagel, One-parameter semigroups for linear evolution equations. Springer-Verlag, New York (2000). | ||||
| Prerequisites / Notice | Mandatory prerequisites: Functional analysis Start of lectures: Friday, September 23, 2016 For more details, please follow the link in the Learning materials section. | ||||
| 401-4657-00L | Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | 6 credits | 3V + 1U | A. Jentzen | |
| Abstract | Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables. | ||||
| Learning objective | The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues. | ||||
| Content | Generation of random numbers Monte Carlo methods for the numerical integration of random variables Stochastic processes and Brownian motion Stochastic ordinary differential equations (SODEs) Numerical approximations of SODEs Multilevel Monte Carlo methods for SODEs Applications to computational finance: Option valuation | ||||
| Lecture notes | Lecture Notes are available in the lecture homepage (please follow the link in the Learning materials section). | ||||
| Literature | P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. | ||||
| Prerequisites / Notice | Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday, September 21, 2016 For more details, please follow the link in the Learning materials section. | ||||
| 401-5650-00L | Zurich Colloquium in Applied and Computational Mathematics | 0 credits | 2K | R. Abgrall, H. Ammari, R. Hiptmair, A. Jentzen, S. Mishra, S. Sauter, C. Schwab | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||