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A celebration of 300 years of stochastics
Freiburg and Basel, May 21 - 24, 2013

Jean Jacod, Paris   Basel, May 23, 2013, 15:00–16:00
Lévy, Itô, Doob, Meyer and Beyond: Birth and Development of Semimartingales
Abstract: The theory of semimartingales took more than 40 years to reach its full extension, and the main aim of the talk is to give an account of how this happened, and of the main steps on the road. Although in many respects the theory is now achieved, it still undergoes interesting developments on some specific points, and our secondary aim is to sketch some of these recent extensions.
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Tom Kurtz, Madison    Freiburg, May 24, 2013, 15:30–16:30
Diffusion Approximations for Markov Processes with Multiple Time Scales
Abstract: Motivated by models from systems biology, techniques for deriving diffusion approximations will be discussed. Fluctuations in the process may arise both from random sampling and from rapid variation in the natural drift of the process. Classical martingale methods are exploited to deal with both sources simultaneously. Examples include Michaelis-Menten type enzyme reactions as well as models of more complicated reaction networks. The talk is based on joint work with Hye-Won Kang and Lea Popovic.
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Michael Sørensen, Copenhagen   Freiburg, May 22, 2013, 16:30–17:30
Statistics for Stochastic Differential Equations – Past and Present
Abstract: The first statistical methods for stochastic differential equations were developed for continuous-time data, where an entire trajectory is assumed to be observed in an interval. Such data cannot be obtained in practice, but an explicit likelihood function is given by the Girsanov formula, and a beautiful theory was developed, in particular for exponential families of diffusion processes. Although this theory is not directly applicable in practice, it has in several ways informed the development of statistical methods for discretely sampled stochastic differential equations, and the continuous-time likelihood plays an important role in some modern approaches to likelihood inference for discrete-time observations. For discrete-time data, there is usually no explicit expression for the likelihood function, which is a product of transition densities. Therefore, the likelihood function must be approximated, which can be done in several ways. The talk will review these developments, including recent methods for simulation-based likelihood inference.
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