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This volume collects selected papers from the 7th High Dimensional Probability meeting held at the Institut d'Études Scientifiques de Cargèse (IESC) in Corsica, France. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other subfields of mathematics, statistics, and computer science. These include random matrices, nonparametric statistics, empirical processes, statistical learning theory, concentration of measure phenomena, strong and weak approximations, functional estimation, combinatorial optimization, and random graphs. The contributions in this volume show that HDP theory continues to thrive and develop new tools, methods, techniques and perspectives to analyze random phenomena.

Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probabilities --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

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In addition to its further exploration of the subject of peacocks, introduced in recent Séminaires de Probabilités, this volume continues the series’ focus on current research themes in traditional topics such as stochastic calculus, filtrations and random matrices. Also included are some particularly interesting articles involving harmonic measures, random fields and loop soups. The featured contributors are Mathias Beiglböck, Martin Huesmann and Florian Stebegg, Nicolas Juillet, Gilles Pags, Dai Taguchi, Alexis Devulder, Mátyás Barczy and Peter Kern, I. Bailleul, Jürgen Angst and Camille Tardif, Nicolas Privault, Anita Behme, Alexander Lindner and Makoto Maejima, Cédric Lecouvey and Kilian Raschel, Christophe Profeta and Thomas Simon, O. Khorunzhiy and Songzi Li, Franck Maunoury, Stéphane Laurent, Anna Aksamit and Libo Li, David Applebaum, and Wendelin Werner. .

Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Math --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Science --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities

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This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the population is bound to go extinct in finite time. It is explained when the interaction is strong enough so that the extinction time remains finite, when the ancestral population at time 0 goes to infinity. The material could be used for teaching stochastic processes, together with their applications. Étienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, stochastic partial differential equations, and probabilistic models in evolutionary biology and population genetics. He obtained his PhD in 1975 at University of Paris-Sud.

Mathematics. --- Ecology. --- Probabilities. --- Biomathematics. --- Mathematical and Computational Biology. --- Probability Theory and Stochastic Processes. --- Theoretical Ecology/Statistics. --- Biology --- Probability --- Statistical inference --- Balance of nature --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Math --- Mathematics --- Ecology --- Distribution (Probability theory. --- Environmental sciences --- Population biology --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Branching processes. --- Ecology . --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course.

Mathematics. --- Mathematical statistics. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Probability and Statistics in Computer Science. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Probability --- Statistical inference --- Mathematics --- Statistics, Mathematical --- Math --- Econometrics --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistics --- Probabilities --- Sampling (Statistics) --- Science --- Distribution (Probability theory. --- Computer science. --- Informatics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics .

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This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.

Mathematics. --- Economics, Mathematical. --- Actuarial science. --- Mathematical models. --- Probabilities. --- Quantitative Finance. --- Mathematical Modeling and Industrial Mathematics. --- Probability Theory and Stochastic Processes. --- Actuarial Sciences. --- Probability --- Statistical inference --- Models, Mathematical --- Economics --- Mathematical economics --- Math --- Mathematics --- Finance. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Currency question --- Business mathematics. --- Economics, Mathematical . --- Statistics --- Insurance --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Simulation methods --- Econometrics --- Methodology