Stochastics

A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable.

The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline.

Matrix-analytic and related methods have become recognized as an important and fundamental approach for the mathematical analysis of general classes of complex stochastic models.

This book covers the method of metric distances and its application in probability theory and other fields.

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Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics.

Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks.

The book is composed of two main parts: mathematical background and queueing systems with applications.

Mathematical Statistics for Economics and Business, Second Edition, provides a comprehensive introduction to the principles of mathematical statistics which underpin statistical analyses in the fields of economics, business, and econometrics.

This book collects some recent developments in stochastic control theory with applications to financial mathematics.

This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering.

Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras.

This book is for a first course in stochastic processes taken by undergraduates or master's students who have had a course in probability theory.

The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973.

For the first two editions of the book Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises.

The book presents an introduction to Stochastic Processes including Markov Chains, Birth and Death processes, Brownian motion and Autoregressive models.

Stochastic Optimal Control (SOC)-a mathematical theory concerned with minimizing a cost (or maximizing a payout) pertaining to a controlled dynamic process under uncertainty-has proven incredibly helpful to understanding and predicting debt crises and evaluating proposed financial regulation and risk management.

This new edition of the well established text Scheduling - Theory, Algorithms, and Systems provides an up-to-date coverage of important theoretical models in the scheduling literature as well as significant scheduling problems that occur in the real world.

This research monograph summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian Cycle and the Travelling Salesman Problems - into convex domains where continuum analysis can be carried out.

In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen.

Inequalities of Ostrowski and Trapezoidal Type for Functions of Selfadjoint Operators on Hilbert Spaces presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of bounded Selfadjoint operators on complex Hilbert spaces.

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator.

This brief offers a broad, yet concise, coverage of portfolio choice, containing both application-oriented and academic results, along with abundant pointers to the literature for further study.

This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view.

This book offers an analytical rather than measure-theoretical approach to the derivation of the partial differential equations of nonlinear filtering theory.

This textbook focuses on stochastic analysis in systems biology containing both the theory and application.

This monograph and translation from the Russian describes in detail and comments on the fundamentals of metrology.

The main aim of this book is to present recent results concerning inequalities of the Jensen, Cebysev and Gruss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces.

This text on stochastic processes and their applications is based on a set of lectures given during the past several years at the University of California, Santa Barbara (UCSB).

Models to forecast changes in mortality, morbidity, and disability in elderly populations are essential to national and state policies for health and welfare programs.

Modern astronomy has been characterized by an enormous growth in data acquisition - from new technologies in telescopes, detectors, and computation.

All students and professionals in statistics should refer to this volume as it is a handy reference source for statistical formulas and information on basic probability distributions.

The 13th Symposium on the Interface continued this series after a one year pause.

This IMA Volume in Mathematics and its Applications STOCHASTIC DIFFERENTIAL SYSTEMS, STOCHASTIC CONTROL THEORY AND APPLICATIONS is the proceedings of a workshop which was an integral part of the 1986-87 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS.

This IMA Volume in ~athematics and its Applications PERCOLATION THEORY AND ERGODIC THEORY OF INFINITE PARTICLE SYSTEMS represents the proceedings of a workshop which was an integral part of the 19R4-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: naniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaoo for planning and implementing an exciting and stimulating year-long program.

This IMA Volume in Mathematics and its Applications STOCHASTIC MODELS IN GEOSYSTEMS is based on the proceedings of a workshop with the same title and was an integral part of the 1993-94 IMA program on "e;Emerging Applications of Probability.

This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas- tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "e;Emerging Applications of Probability.

This IMA Volume in Mathematics and its Applications RANDOM MEDIA represents the proceedings of a workshop which was an integral part of the 1984-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: Daniel Stroock (Chairman) \~ende 11 Fl emi ng Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program.

This book brings together the personal accounts and reflections of nineteen mathematical model-builders, whose specialty is probabilistic modelling.

A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion.

In this book we study Markov random functions of several variables.

It appears that we live in an age of disasters: the mighty Missis- sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening.

The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume.

This book contains selected and refereed contributions to the "e;Inter- national Symposium on Probability and Bayesian Statistics"e; which was orga- nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria.

The authors, Dominique Ladiray and Benoit Quenneville, provide a unique and comprehensive r~view of the X-11 Method of seasonal adjustment.

These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability.