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The Research Network on ""Interacting stochastic systems of high complexity"" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interwea

Stochastic systems. --- Stochastic analysis. --- Statistical physics. --- Probabilities. --- Science --- Mathematical models --- Industrial applications. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Natural science --- Science of science --- Sciences --- Physics --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Systems, Stochastic --- System analysis --- Statistical methods --- Distribution (Probability theory. --- Mathematics. --- Mathematical physics. --- Statistics. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Mathematical and Computational Biology. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Methods in Physics. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Math --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Physical mathematics --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Physics. --- Statistics . --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Biology --- Engineering --- Engineering analysis

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Large deviations

Probability theory --- Large deviations. --- Limit theorems (Probability theory) --- 519.21 --- 519.22 --- Large deviations --- Deviations, Large --- Statistics --- 519.22 Statistical theory. Statistical models. Mathematical statistics in general --- Statistical theory. Statistical models. Mathematical statistics in general --- 519.21 Probability theory. Stochastic processes --- Probability theory. Stochastic processes --- Probabilities

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Probability theory

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1 2 Jean-Dominique Deuschel and Andreas Greven 1 Fakult¨ at II - Mathematik und Naturwissenschaften, Institut fur ¨ Mathematik, Technische Universit¨ at Berlin, Straße des 17. Juni 136, D-10623 Berlin Tel. (0049 30) 314-25193, Fax: (0049 30) 314-21695 deuschel@math. tu-berlin. de 2 1 Mathematisches Institut, Bismarckstr. 1 , D-91054 Erlangen, 2 Tel. (0049 9131) 85-22454, Fax (0049 9131) 85-26214 This volume collects original work and reviews on work in the ?eld of pro- bilitywhichtookplacewithintheframeworkoftheDFG-Schwerpunkt:Int- acting stochastic systems of high complexity. This research network started in May 1997 and was funded till May 2003. In this network between 20-30 (depending on the 2-year periods of grant renewal) groups from probab- ity, statistical physics and mathematical statistics within Germany were - tive. An extensive international collaboration was an essential part of this network and here particularly intense contacts were built up between the DFG-Schwerpunkt and EURANDOM, a European institute for research in stochastics, which was founded in 1997. This partnership reached from joint workshops and colloquia to collaborations on speci?c projects. The key scienti?c idea which was behind the research network was to - plore and develop the connections between research in in?nite dimensional stochastic analysis, statistical physics (Gibbs measures, random media), s- tial population models from mathematical biology, complex models of ?n- cial markets or of stochastic models with interacting components in other sciences as for example in climatology.

Operational research. Game theory --- Mathematics --- Mathematical physics --- Statistical physics --- Biomathematics. Biometry. Biostatistics --- Engineering sciences. Technology --- statistische kwaliteitscontrole --- industriële statistieken --- toegepaste wiskunde --- biomathematica --- stochastische analyse --- biometrie --- wiskunde --- fysica --- kansrekening

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