This volume presents an extensive overview of all major modern trends in applications of probability and stochastic analysis. It will be a great source of inspiration for designing new algorithms, modeling procedures and experiments. Accessible to researchers, practitioners, as well as graduate and postgraduate students, this volume presents a variety of new tools, ideas and methodologies in the fields of optimization, physics, finance, probability, hydrodynamics, reliability, decision making, mathematical finance, mathematical physics and economics. Contributions to this Work include those of selected speakers from the international conference entitled “Modern Stochastics: Theory and Applications III,” held on September 10 –14, 2012 at Taras Shevchenko National University of Kyiv, Ukraine. The conference covered the following areas of research in probability theory and its applications: stochastic analysis, stochastic processes and fields, random matrices, optimization methods in probability, stochastic models of evolution systems, financial mathematics, risk processes and actuarial mathematics and information security.

Probability theory has grown from a modest study of simple games of change to a subject with application in almost every branch of knowledge and science. In this exciting book, a number of distinguished probabilists discuss their current work and applications in an easily understood manner. Chapters show that new directions in probability have been suggested by the application of probability to other fields and other disciplines of mathematics. The study of polymer chains in chemistry led to the study of self-avoiding random walks; the study of the Ising model in physics and models for epidemics in biology led to the study of the probability theory of interacting particle systems. The stochastic calculus has allowed probabilists to solve problems in classical analysis, in theory of investment, and in engineering. The mathematical formulation of game theory has led to new insights into decisions under uncertainty. These new developments in probability are vividly illustrated throughout the book.

This book introduces stochastic processes and their applications for students in engineering, industrial statistics, science, operations research, business, and finance. It provides the theoretical foundations for modeling time-dependent random phenomena encountered in these disciplines. Through numerous science and engineering-based examples and exercises, the author presents the subject in a comprehensible, practically oriented way, but he also includes some important proofs and theoretically challenging examples and exercises that will appeal to more mathematically minded readers. Solutions to most of the exercises are included either in an appendix or within the text.

This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)