Credit: Anna Logue
Monte Carlo Methoden II
Andreas Neuenkirch
Vorlesung mit Übung (MSc, 6 ECTS)
In dieser Veranstaltung werden wir u.a. folgende weiterführende Themen der stochastischen Numerik behandeln:
- Quantisierung
- Monte Carlo Verfahren für lineare Gleichungssysteme
- Sphärischer Prozess & Dirichlet Problem
Termine etc.
- Erste Vorlesung: Donnerstag, 7.9.2023,13:45 -- 15:15, C 014 Hörsaal (A 5, 6 Bauteil C)
- Erste Übung: Donnerstag, 14.9.2023, 15:30 -- 17:00, C 014 Hörsaal (A 5, 6 Bauteil C)
- Ab Woche 2: Vorlesung am Donnerstag um 15:30 in C 014, Übung im Anschluss
- Prüfungszulassung: 50 % der Abgabenaufgabenpunkte; Zweierabgabe möglich
- Termine für die mündlichen Prüfungen werden noch bekanntgegeben
Literatur
- Lloyd, S.P. (1982) Least Squares Quantization in PCM. IEEE Transactions on Information Theory, 28, 129–137.
- Foundations of Quantization for Probability Distributions, Lecture Notes in Mathematics, Siegfried Graf, Harald Luschgy, Springer, 2007
- Numerical Probability, An Introduction with Applications to Finance, Gilles Pagès, Springer. 2018
- J. Kieffer, Exponential rate of convergence for Lloyd's method I, in IEEE Transactions on Information Theory, vol. 28, no. 2, pp. 205–210, March 1982
- George Forsythe, Richard Leibler, Matrix inversion by a Monte Carlo method, Math. Tables and Other Aids to Computation, 4 (1950), 127–129
- W. Wasow, A note on the inversion of matrices by random walks, Math. Tables and Other Aids to Computation, 6 (1952), 78–81
- J. Curtiss, A theoretical comparison of the efficiencies of two classical methods and a Monte Carlo method for computing one component of the solution of a set of linear algebraic equations, John Wiley and Sons, Inc., New York, 1956, 191–233
- Introduction to Probability. Charles M. Grinstead and J. Laurie Snell, American Mathematical Society; 2nd Revised edition (July 1, 1997)
- Mervin E. Muller. “Some Continuous Monte Carlo Methods for the Dirichlet Problem.” Ann. Math. Statist. 27 (3) 569 – 589, September, 1956
- Thomas Müller-Gronbach, Erich Novak, Klaus Ritter, Monte Carlo-Algorithmen, Springer Berlin, Heidelberg 2012
- Minoru Motoo, 1959. “Some evaluations for continuous Monte Carlo method by using Brownian hitting process,” Annals of the Institute of Statistical Mathematics, vol. 11(1), pages 49–54, February