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This volume contains twenty-eight refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 30 to June 3, 2005. The seminar focused mainly on stochastic partial differential equations, random dynamical systems, infinite-dimensional analysis, approximation problems, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance. Contributors: Y. Asai, J.-P. Aubin, C. Becker, M. Benaïm, H. Bessaih, S. Biagini, S. Bonaccorsi, N. Bouleau, N. Champagnat, G. Da Prato, R. Ferrière, F. Flandoli, P. Guasoni, V.B. Hallulli, D. Khoshnevisan, T. Komorowski, R. Léandre, P. Lescot, H. Lisei, J.A. López-Mimbela, V. Mandrekar, S. Méléard, A. Millet, H. Nagai, A.D. Neate, V. Orlovius, M. Pratelli, N. Privault, O. Raimond, M. Röckner, B. Rüdiger, W.J. Runggaldier, P. Saint-Pierre, M. Sanz-Solé, M. Scheutzow, A. Soós, W. Stannat, A. Truman, T. Vargiolu, A.E.P. Villa, A.B. Vizcarra, F.G. Viens, J.-C. Zambrini, B. Zegarlinski.

Stochastic analysis --- Random fields --- Business mathematics --- Fields, Random --- Stochastic processes --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Mathematics --- Distribution (Probability theory. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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This volume contains refereed research or review papers presented at the 6th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, in May 2008. The seminar focused mainly on stochastic partial differential equations, especially large deviations and control problems, on infinite dimensional analysis, particle systems and financial engineering, especially energy markets and climate models. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance. Contributors: S. Albeverio S. Ankirchner V. Bogachev R. Brummelhuis Z. Brzeźniak R. Carmona C. Ceci J.M. Corcuera A.B. Cruzeiro G. Da Prato M. Fehr D. Filipović B. Goldys M. Hairer E. Hausenblas F. Hubalek H. Hulley P. Imkeller A. Jakubowski A. Kohatsu-Higa A. Kovaleva E. Kyprianou C. Léonard J. Lörinczi A. Malyarenko B. Maslowski J.C. Mattingly S. Mazzucchi L. Overbeck E. Platen M. Röckner M. Romito T. Schmidt R. Sircar W. Stannat K.-T. Sturm A. Toussaint L. Vostrikova J. Woerner Y. Xiao J.-C. Zambrini.

Random fields -- Congresses. --- Random fields. --- Stochastic analysis -- Congresses. --- Stochastic analysis. --- Stochastic analysis --- Random fields --- Mathematics --- Distribution (Probability theory) --- Physical Sciences & Mathematics --- Mathematical Statistics --- Fields, Random --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Stochastic processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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This is the second volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters, which is published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.   The expository articles in this second volume cover two important topics in the area of Lévy processes. The first article by Serge Cohen reviews the most important findings on fractional Lévy fields to date in a self-contained piece, offering a theoretical introduction as well as possible applications and simulation techniques. The second article, by Alexey Kuznetsov, Andreas E. Kyprianou, and Victor Rivero, presents an up to date account of the theory and application of scale functions for spectrally negative Lévy processes, including an extensive numerical overview.

Lâevy processes --- Random fields --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Mathematical Statistics --- Lévy processes. --- Random fields. --- Mathematics. --- Probabilities. --- Mathematics, general. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Fields, Random --- Stochastic processes --- Random walks (Mathematics) --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Levy processes.

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The book is concerned with the statistical theory for locating spatial sensors. It bridges the gap between spatial statistics and optimum design theory. After introductions to those two fields the topics of exploratory designs and designs for spatial trend and variogram estimation are treated. Special attention is devoted to describing new methodologies to cope with the problem of correlated observations. A great number of relevant references are collected and put into a common perspective. The theoretical investigations are accompanied by a practical example, the redesign of an Upper-Austrian air pollution monitoring network. A reader should be able to find respective theory and recommendations on how to efficiently plan a specific purpose spatial monitoring network. The third edition takes into account the rapid development in the area of spatial statistics by including new relevant research and references. The revised edition contains additional material on design for detecting spatial dependence and for estimating parametrized covariance functions. .

Experimental design. --- Random fields. --- Fields, Random --- Stochastic processes --- Design of experiments --- Statistical design --- Mathematical optimization --- Research --- Science --- Statistical decision --- Statistics --- Analysis of means --- Analysis of variance --- Experiments --- Methodology --- Regional economics. --- Statistics. --- Environmental sciences. --- Geography. --- Regional/Spatial Science. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Math. Appl. in Environmental Science. --- Earth Sciences, general. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Cosmography --- Earth sciences --- World history --- Environmental science --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Economics --- Regional planning --- Regionalism --- Space in economics --- Spatial economics. --- Statistics . --- Earth sciences. --- Geosciences --- Environmental sciences --- Physical sciences --- Spatial economics --- Regional economics

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This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. The three parts to the monograph are quite distinct. Part I presents a user-friendly yet comprehensive background to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities. Part II gives a quick review of geometry, both integral and Riemannian, to provide the reader with the material needed for Part III, and to give some new results and new proofs of known results along the way. Topics such as Crofton formulae, curvature measures for stratified manifolds, critical point theory, and tube formulae are covered. In fact, this is the only concise, self-contained treatment of all of the above topics, which are necessary for the study of random fields. The new approach in Part III is devoted to the geometry of excursion sets of random fields and the related Euler characteristic approach to extremal probabilities. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory. These applications, to appear in a forthcoming volume, will cover areas as widespread as brain imaging, physical oceanography, and astrophysics.

Mathematics. --- Probability Theory and Stochastic Processes. --- Statistics, general. --- Geometry. --- Mathematical Methods in Physics. --- Distribution (Probability theory). --- Mathematical physics. --- Statistics. --- Mathématiques --- Géométrie --- Distribution (Théorie des probabilités) --- Physique mathématique --- Statistique --- Global differential geometry. --- Random fields. --- Stochastic geometry. --- Random fields --- Global differential geometry --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Fields, Random --- Probabilities. --- Physics. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Euclid's Elements --- Math --- Science --- Geometry, Differential --- Stochastic processes --- Distribution (Probability theory. --- Physical mathematics --- Physics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistics .