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Feynman-Kac Formulae
This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.
Mean Field Simulation for Monte Carlo Integration
In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle fi...
Stochastic Processes
Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.
Numerical Methods in Finance
Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.
Fundamentals of Stochastic Filtering
This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.
Statistical Modeling and Analysis for Complex Data Problems
This book reviews some of today’s more complex problems, and reflects some of the important research directions in the field. Twenty-nine authors – largely from Montreal’s GERAD Multi-University Research Center and who work in areas of theoretical statistics, applied statistics, probability theory, and stochastic processes – present survey chapters on various theoretical and applied problems of importance and interest to researchers and students across a number of academic domains.
An Introduction to Wishart Matrix Moments
This book, written in lecture note style, provides a comprehensive and self-contained introduction to the analysis of Wishart matrix moments. It can act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition of Wishart matrix moments.
Lawrence Kohlberg – An Introduction
Lawrence Kohlberg (1927-1987) was one of the key figures in generating theories of human development. Following James Mark Baldwin and Jean Piaget, he designed a research program in order to understand moral development – which he viewed as justice development -, during the life-span. With the help of dilemma-interviews and a comprehensive scoring manual, Kohlberg looked into the stage of development and the moral point of view of children, adolescents and adults both in the United States and abroad. Related herewith, he discussed central topics, such as the relationship be¬tween judgment and action, the transnational universality of moral development, and gender-related morality. His innovative interdisciplinary work embraced the fields of developmental psychology, philosophy, and education among others. His research was inspiring in many aspects and will be inspiring for the years to come.
The Practice of Moral Judgment
Barbara Herman argues for a radical shift in the way we perceive Kant's ethics. She convincingly reinterprets the key texts, at once allowing Kant to mean what he says while showing that what Kant says makes good moral sense. She urges us to abandon the tradition that describes Kantian ethics as a deontology, a moral system of rules of duty. She finds the central idea of Kantian ethics not in duty but in practical rationality as a norm of unconditioned goodness. This book both clarifies Kant's own theory and adds programmatic vitality to modern moral philosophy.
