General Stochastic Measures
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General Stochastic Measures
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Author : Vadym M. Radchenko
language : en
Publisher: John Wiley & Sons
Release Date : 2022-08-23
General Stochastic Measures written by Vadym M. Radchenko and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-23 with Mathematics categories.
This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as square-integrable martingales and fractional Brownian motion, as well as alpha-stable processes. SMs include many well-known stochastic integrators as partial cases. General Stochastic Measures provides a comprehensive theoretical overview of SMs, including the basic properties of the integrals of real functions with respect to SMs. A number of results concerning the Besov regularity of SMs are presented, along with equations driven by SMs, types of solution approximation and the averaging principle. Integrals in the Hilbert space and symmetric integrals of random functions are also addressed. The results from this book are applicable to a wide range of stochastic processes, making it a useful reference text for researchers and postgraduate or postdoctoral students who specialize in stochastic analysis.
Stochastic Integration
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Author : Michel Metivier
language : en
Publisher: Academic Press
Release Date : 2014-07-10
Stochastic Integration written by Michel Metivier and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Integration focuses on the processes, methodologies, and approaches involved in stochastic integration. The publication first takes a look at the Ito formula, stochastic integral equations, and martingales and semimartingales. Discussions focus on Meyer process and decomposition theorem, inequalities, examples of stochastic differential equations, general stochastic integral equations, and applications of the Ito formula. The text then elaborates on stochastic measures, including stochastic measures and related integration and the Riesz representation theorem. The manuscript tackles the special features of infinite dimensional stochastic integration, as well as the isometric integral of a Hubert-valued square integrable martingale, cylindrical processes, and stochastic integral with respect to 2-cylindrical martingales with finite quadratic variation. The book is a valuable reference for mathematicians and researchers interested in stochastic integration.
Stochastic Processes General Theory
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Author : Malempati M. Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Stochastic Processes General Theory written by Malempati M. Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.
Statistics Of Random Processes Ii
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Author : Robert S. Liptser
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Statistics Of Random Processes Ii written by Robert S. Liptser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW
Topics In Stochastic Processes
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Author : Robert B. Ash
language : en
Publisher: Academic Press
Release Date : 2014-06-20
Topics In Stochastic Processes written by Robert B. Ash and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-20 with Mathematics categories.
Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.
Statistics Of Random Processes
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Author : Robert Liptser
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Statistics Of Random Processes written by Robert Liptser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
These volumes cover non-linear filtering (prediction and smoothing) theory and its applications to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. Also presented is the theory of martingales, of interest to those who deal with problems in financial mathematics. These editions include new material, expanded chapters, and comments on recent progress in the field.
Stochastic Calculus And Applications
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Author : Samuel N. Cohen
language : en
Publisher: Birkhäuser
Release Date : 2015-11-18
Stochastic Calculus And Applications written by Samuel N. Cohen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Mathematics categories.
Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)
An Introduction To The Theory Of Point Processes
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Author : Daryl J. Daley
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
An Introduction To The Theory Of Point Processes written by Daryl J. Daley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Stochastic point processes are sets of randomly located points in time, on the plane or in some general space. This book provides a general introduction to the theory, starting with simple examples and an historical overview, and proceeding to the general theory. It thoroughly covers recent work in a broad historical perspective in an attempt to provide a wider audience with insights into recent theoretical developments. It contains numerous examples and exercises. This book aims to bridge the gap between informal treatments concerned with applications and highly abstract theoretical treatments.
Stochastic Integration In Banach Spaces
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Author : Vidyadhar Mandrekar
language : en
Publisher: Springer
Release Date : 2014-12-03
Stochastic Integration In Banach Spaces written by Vidyadhar Mandrekar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-03 with Mathematics categories.
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups.
Probability Metrics And The Stability Of Stochastic Models
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Author : Svetlozar T. Rachev
language : en
Publisher:
Release Date : 1991-05-13
Probability Metrics And The Stability Of Stochastic Models written by Svetlozar T. Rachev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-05-13 with Mathematics categories.
Concentrates on four specialized research directions as well as applications to different problems of probability theory. These include: description of the basic structure of p. metrics, analysis of the topologies in the space of probability measures generated by different types of p. metrics, characterization of the ideal metrics for the given problem and investigations of the main relationships between different types of p. metrics. The presentation here is given in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases.