Foundations of Stochastic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Stochastic Analysis write by M. M. Rao. This book was released on 2011-01-01. Foundations of Stochastic Analysis available in PDF, EPUB and Kindle. Stochastic analysis involves the study of a process involving a randomly determined sequence of observations, each of which represents a sample of one element of probability distribution. This volume considers fundamental theories and contrasts the natural interplay between real and abstract methods. Starting with the introduction of the basic Kolmogorov-Bochner existence theorem, the text explores conditional expectations and probabilities as well as projective and direct limits. Subsequent chapters examine several aspects of discrete martingale theory, including applications to ergodic theory, likelihood ratios, and the Gaussian dichotomy theorem. Prerequisites include a standard measure theory course. No prior knowledge of probability is assumed; therefore, most of the results are proved in detail. Each chapter concludes with a problem section that features many hints and facts, including the most important results in information theory.
Fundamentals of Stochastic Filtering
Fundamentals of Stochastic Filtering - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fundamentals of Stochastic Filtering write by Alan Bain. This book was released on 2008-10-08. Fundamentals of Stochastic Filtering available in PDF, EPUB and Kindle. 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.
Foundations of Infinitesimal Stochastic Analysis
Foundations of Infinitesimal Stochastic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Infinitesimal Stochastic Analysis write by K.D. Stroyan. This book was released on 2011-08-18. Foundations of Infinitesimal Stochastic Analysis available in PDF, EPUB and Kindle. 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.
Applied Stochastic Analysis
Applied Stochastic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applied Stochastic Analysis write by Weinan E. This book was released on 2021-09-22. Applied Stochastic Analysis available in PDF, EPUB and Kindle. 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.
Stochastic Simulation and Monte Carlo Methods
Stochastic Simulation and Monte Carlo Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Simulation and Monte Carlo Methods write by Carl Graham. This book was released on 2013-07-16. Stochastic Simulation and Monte Carlo Methods available in PDF, EPUB and Kindle. 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.
