# 401-4606-00L Numerical Analysis of Stochastic Partial Differential Equations

Semester | Spring Semester 2015 |

Lecturers | A. Jentzen |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | In this course solutions of semilinear stochastic partial differential equations (SPDEs) and some of their numerical approximation methods are investigated. Semilinear SPDEs, in particular, arise in models from neurobiology, population genetics and quantum field theory. |

Objective | The aim of this course is to teach the students a decent knowledge on solutions of semilinear stochastic partial differential equations (SPDEs), on some numerical approximation methods for such equations and on the functional analytic concepts used to formulate and study such equations. |

Content | The course includes content on nuclear operators, on Hilbert-Schmidt operators, on semigroups of bounded linear operators, on Gronwall-type inequalities, on Hilbert space valued random variables, on Hilbert space valued stochastic processes, on infinite dimensional Wiener processes, on the stochastic integration with respect to infinite dimensional Wiener processes, on mild solutions of semilinear stochastic partial differential equations (SPDEs) of the evolutionary type, on spatial discretizations of such SPDEs as well as on temporal discretizations of such SPDEs. Semilinear SPDEs, in particular, arise in models from neurobiology, population genetics and quantum field theory. |

Lecture notes | Lecture notes will be available. |

Literature | 1. Stochastic Equations in Infinite Dimensions G. Da Prato and J. Zabczyk Cambridge Univ. Press (1992) 2. Taylor Approximations for Stochastic Partial Differential Equations A. Jentzen and P.E. Kloeden Siam (2011) 3. Numerical Solution of Stochastic Differential Equations P.E. Kloeden and E. Platen Springer Verlag (1992) 4. A Concise Course on Stochastic Partial Differential Equations C. Prévôt and M. Röckner Springer Verlag (2007) 5. Galerkin Finite Element Methods for Parabolic Problems V. Thomée Springer Verlag (2006) |

Prerequisites / Notice | Functional analysis, probability theory, stochastic processes, Brownian motion and Ito stochastic calculus in finite dimensions |