Zapraszamy kolejne wykłady prof. Jeffreya Collamore\'a z Kopenhagi: 29 kwietnia 2013 r., godz. 14:15, 6 maja 2013 r., godz. 14:15, 9 maja 2013 r., godz. 16:15, 16 maja 2013 r., godz. 16:15. Wszystkie wykłady odbędą się w sali A. Temat: Large Deviations: Theory and Applications Abstrakt: Recently, large deviations has been an active area of applied probability. Originally motivated by problems in statistics and insurance mathematics, the mode theory has evolved to encompass a variety of other areas, including information theory, queuing theory, rare event simulation, genetic sequencing, and statistical physics. The goal of these lectures will be to give a general introduction to the theory. We will begin with the most basic result, namely Cramer\'s theorem, and describe its extensions to more general processes and more general problems involving sample paths. We will also discuss large deviation results for the first passage times of a multidimensional random walk, and describe how these theoretical results can be adapted to computational problems involving importance sampling. We will illustrate this theory with a variety of examples.
