Foundations Of Stochastic Analysis

Author : M. M. Rao
Publisher : Courier Corporation
ISBN 13 : 0486296539
Total Pages : 320 pages
Book Rating : 4.31/5 ( download)

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Download or read book Foundations of Stochastic Analysis written by M. M. Rao and published by Courier Corporation. This book was released on 2013-04-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Weinan E
Publisher : American Mathematical Soc.
ISBN 13 : 1470449331
Total Pages : 305 pages
Book Rating : 4.39/5 ( download)

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Download or read book Applied Stochastic Analysis written by Weinan E and published by American Mathematical Soc.. This book was released on 2019-05-28 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.

Author : K.D. Stroyan
Publisher : Elsevier
ISBN 13 : 0080960421
Total Pages : 491 pages
Book Rating : 4.25/5 ( download)

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Download or read book Foundations of Infinitesimal Stochastic Analysis written by K.D. Stroyan and published by Elsevier. This book was released on 2011-08-18 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alan Bain
Publisher : Springer Science & Business Media
ISBN 13 : 0387768963
Total Pages : 395 pages
Book Rating : 4.60/5 ( download)

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Download or read book Fundamentals of Stochastic Filtering written by Alan Bain and published by Springer Science & Business Media. This book was released on 2008-10-08 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Barry Nelson
Publisher : Springer Science & Business Media
ISBN 13 : 146146160X
Total Pages : 285 pages
Book Rating : 4.09/5 ( download)

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Download or read book Foundations and Methods of Stochastic Simulation written by Barry Nelson and published by Springer Science & Business Media. This book was released on 2013-01-31 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Paul Malliavin
Publisher : Springer
ISBN 13 : 3642150748
Total Pages : 346 pages
Book Rating : 4.46/5 ( download)

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Download or read book Stochastic Analysis written by Paul Malliavin and published by Springer. This book was released on 2015-06-12 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Carl Graham
Publisher : Springer Science & Business Media
ISBN 13 : 3642393632
Total Pages : 264 pages
Book Rating : 4.31/5 ( download)

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Download or read book Stochastic Simulation and Monte Carlo Methods written by Carl Graham and published by Springer Science & Business Media. This book was released on 2013-07-16 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Malempati Madhusudana Rao
Publisher :
ISBN 13 : 9780125808507
Total Pages : 295 pages
Book Rating : 4.0X/5 ( download)

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Download or read book Foundations of Stochastic Analysis written by Malempati Madhusudana Rao and published by . This book was released on 1981-01-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction and generalities; Conditional expectations and probabilities; Projective and direct limits; Martingales and likelihood ratios; Abstract martingales and applications.

Author : Elton P. Hsu
Publisher : American Mathematical Soc.
ISBN 13 : 0821808028
Total Pages : 297 pages
Book Rating : 4.23/5 ( download)

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Download or read book Stochastic Analysis on Manifolds written by Elton P. Hsu and published by American Mathematical Soc.. This book was released on 2002 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concerned with probability theory, Elton Hsu's study focuses primarily on the relations between Brownian motion on a manifold and analytical aspects of differential geometry. A key theme is the probabilistic interpretation of the curvature of a manifold

Author : M. M. Rao
Publisher : Elsevier
ISBN 13 : 1483269310
Total Pages : 310 pages
Book Rating : 4.13/5 ( download)

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Download or read book Foundations of Stochastic Analysis written by M. M. Rao and published by Elsevier. This book was released on 2014-07-10 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.