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Author : M. M. Rao
Publisher : Courier Corporation
Page : 320 pages
File Size : 54,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9780486296531
This volume considers fundamental theories and contrasts the natural interplay between real and abstract methods. No prior knowledge of probability is assumed. Numerous problems, most with hints. 1981 edition.
Author : K.D. Stroyan,J.M. Bayod
Publisher : Elsevier
Page : 491 pages
File Size : 50,6 Mb
Release : 2011-08-18
Category : Computers
ISBN : 9780080960425
This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
Author : Malempati Madhusudana Rao
Publisher : Unknown
Page : 295 pages
File Size : 53,9 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 012580850X
Introduction and generalities; Conditional expectations and probabilities; Projective and direct limits; Martingales and likelihood ratios; Abstract martingales and applications.
Author : Alan Bain,Dan Crisan
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 46,8 Mb
Release : 2008-10-08
Category : Mathematics
ISBN : 9780387768960
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.
Author : M. M. Rao
Publisher : Elsevier
Page : 310 pages
File Size : 47,8 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483269313
Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and measures. The applications of these conditional expectations and probabilities to Reynolds operators are also considered. The reader is then introduced to projective limits, direct limits, and a generalized Kolmogorov existence theorem, along with infinite product conditional probability measures. The book also considers martingales and their applications to likelihood ratios before concluding with a description of abstract martingales and their applications to convergence and harmonic analysis, as well as their relation to ergodic theory. This monograph should be of considerable interest to researchers and graduate students working in stochastic analysis.
Author : Carl Graham,Denis Talay
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 40,5 Mb
Release : 2013-07-16
Category : Mathematics
ISBN : 9783642393631
In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.
Author : Kiyosi Ito
Publisher : SIAM
Page : 79 pages
File Size : 41,8 Mb
Release : 1984-01-01
Category : Mathematics
ISBN : 1611970237
A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.
Author : Paul Malliavin
Publisher : Springer
Page : 346 pages
File Size : 48,6 Mb
Release : 2015-06-12
Category : Mathematics
ISBN : 9783642150746
In 5 independent sections, this book accounts recent main developments of stochastic analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.
Author : Barry Nelson
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 49,5 Mb
Release : 2013-01-31
Category : Business & Economics
ISBN : 9781461461609
This graduate-level text covers modeling, programming and analysis of simulation experiments and provides a rigorous treatment of the foundations of simulation and why it works. It introduces object-oriented programming for simulation, covers both the probabilistic and statistical basis for simulation in a rigorous but accessible manner (providing all necessary background material); and provides a modern treatment of experiment design and analysis that goes beyond classical statistics. The book emphasizes essential foundations throughout, rather than providing a compendium of algorithms and theorems and prepares the reader to use simulation in research as well as practice. The book is a rigorous, but concise treatment, emphasizing lasting principles but also providing specific training in modeling, programming and analysis. In addition to teaching readers how to do simulation, it also prepares them to use simulation in their research; no other book does this. An online solutions manual for end of chapter exercises is also provided.
Author : K. D. Stroyan
Publisher : Unknown
Page : 0 pages
File Size : 55,7 Mb
Release : 1986
Category : Nonstandard mathematical analysis
ISBN : 004487927X
Author : Howard M. Taylor,Samuel Karlin
Publisher : Academic Press
Page : 410 pages
File Size : 51,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269276
An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
Author : D N Shanbhag,Calyampudi Radhakrishna Rao
Publisher : Gulf Professional Publishing
Page : 990 pages
File Size : 40,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0444500146
This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.
Author : Kun Il Park
Publisher : Springer
Page : 275 pages
File Size : 41,6 Mb
Release : 2017-11-24
Category : Technology & Engineering
ISBN : 9783319680750
This book provides engineers with focused treatment of the mathematics needed to understand probability, random variables, and stochastic processes, which are essential mathematical disciplines used in communications engineering. The author explains the basic concepts of these topics as plainly as possible so that people with no in-depth knowledge of these mathematical topics can better appreciate their applications in real problems. Applications examples are drawn from various areas of communications. If a reader is interested in understanding probability and stochastic processes that are specifically important for communications networks and systems, this book serves his/her need.
Author : Vicenç Méndez,Daniel Campos,Frederic Bartumeus
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 45,5 Mb
Release : 2013-09-18
Category : Science
ISBN : 9783642390104
This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Lévy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitatively and quantitatively describing a wide variety of spatial population ecological phenomena and dynamics, such as invasion fronts and search strategies. Adopting a self-contained, textbook-style approach, the authors provide the elements of statistical physics and stochastic processes on which the modeling of movement ecology is based and systematically introduce the physical characterization of ecological processes at the microscopic, mesoscopic and macroscopic levels. The explicit definition of these levels and their interrelations is particularly suitable to coping with the broad spectrum of space and time scales involved in bio-ecological problems. Including numerous exercises (with solutions), this text is aimed at graduate students and newcomers in this field at the interface of theoretical ecology, mathematical biology and physics.
Author : Yuen-Kwok Chan
Publisher : Cambridge University Press
Page : 627 pages
File Size : 44,8 Mb
Release : 2021-05-27
Category : Mathematics
ISBN : 9781108835435
This book provides a systematic and general theory of probability within the framework of constructive mathematics.