Stochastic Inequalities And Applications
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| Author | : Evariste Giné |
| Publisher | : Birkhäuser |
| Total Pages | : 362 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034880693 |
Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers in the above areas.
| Author | : Feng-Yu Wang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 135 |
| Release | : 2013-08-13 |
| Genre | : Mathematics |
| ISBN | : 1461479347 |
In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.
| Author | : A. Bensoussan |
| Publisher | : Elsevier |
| Total Pages | : 577 |
| Release | : 2011-08-18 |
| Genre | : Mathematics |
| ISBN | : 0080875335 |
Applications of Variational Inequalities in Stochastic Control
| Author | : Albert W. Marshall |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 919 |
| Release | : 2010-11-25 |
| Genre | : Mathematics |
| ISBN | : 0387682767 |
This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. ... This work is a valuable resource!” (Mathematical Reviews). “The authors ... present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of ... Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.
| Author | : Y. L. Tong |
| Publisher | : Academic Press |
| Total Pages | : 256 |
| Release | : 2014-07-10 |
| Genre | : Mathematics |
| ISBN | : 1483269213 |
Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.
| Author | : Avner Friedman |
| Publisher | : Academic Press |
| Total Pages | : 248 |
| Release | : 2014-06-20 |
| Genre | : Mathematics |
| ISBN | : 1483217876 |
Stochastic Differential Equations and Applications, Volume 1 covers the development of the basic theory of stochastic differential equation systems. This volume is divided into nine chapters. Chapters 1 to 5 deal with the basic theory of stochastic differential equations, including discussions of the Markov processes, Brownian motion, and the stochastic integral. Chapter 6 examines the connections between solutions of partial differential equations and stochastic differential equations, while Chapter 7 describes the Girsanov's formula that is useful in the stochastic control theory. Chapters 8 and 9 evaluate the behavior of sample paths of the solution of a stochastic differential system, as time increases to infinity. This book is intended primarily for undergraduate and graduate mathematics students.
| Author | : Moshe Shaked |
| Publisher | : IMS |
| Total Pages | : 434 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780940600294 |
| Author | : Moshe Shaked |
| Publisher | : |
| Total Pages | : 580 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : |
Stochastic orders and inequalities are being used at an accelerated rate in many diverse areas of probability and statistics. This book provides the first unified, systematic, and accessible treatment of stochasticorders, addressing the growing importance of these orders with the presentation of numerous results that illustrate their usefulness and applicability. Ten insightful chapters emphasize the applications by specialists in probability and statistics, economics, operations research, and reliability theory. Applications include multivariate variability, epidemics, comparisons of risk and risk aversion, scheduling, and systems reliability theory.
| Author | : J. Michael Steele |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 303 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468493051 |
Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH
| Author | : Sever S. Dragomir |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 491 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 9401725195 |
It was noted in the preface of the book "Inequalities Involving Functions and Their Integrals and Derivatives", Kluwer Academic Publishers, 1991, by D.S. Mitrinovic, J.E. Pecaric and A.M. Fink; since the writing of the classical book by Hardy, Littlewood and Polya (1934), the subject of differential and integral inequalities has grown by about 800%. Ten years on, we can confidently assert that this growth will increase even more significantly. Twenty pages of Chapter XV in the above mentioned book are devoted to integral inequalities involving functions with bounded derivatives, or, Ostrowski type inequalities. This is now itself a special domain of the Theory of Inequalities with many powerful results and a large number of applications in Numerical Integration, Probability Theory and Statistics, Information Theory and Integral Operator Theory. The main aim of the present book, jointly written by the members of the Vic toria University node of RGMIA (Research Group in Mathematical Inequali ties and Applications, http: I /rgmia. vu. edu. au) and Th. M. Rassias, is to present a selected number of results on Ostrowski type inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadrature for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given.
