Stochastic Analysis

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Stochastic Analysis
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Author : Paul Malliavin
language : en
Publisher: Springer
Release Date : 2015-06-12
Stochastic Analysis written by Paul Malliavin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-12 with Mathematics categories.
This book accounts in 5 independent parts, 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.
Stochastic Analysis In Discrete And Continuous Settings
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Author : Nicolas Privault
language : en
Publisher: Springer
Release Date : 2009-07-14
Stochastic Analysis In Discrete And Continuous Settings written by Nicolas Privault and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-14 with Mathematics categories.
This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.
Stochastic Analysis
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Author : Shigeo Kusuoka
language : en
Publisher: Springer Nature
Release Date : 2020-10-20
Stochastic Analysis written by Shigeo Kusuoka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-20 with Mathematics categories.
This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas. In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob–Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts of the square integrable functions are used in the proof. In stochastic differential equations, the Euler–Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations.
Introduction To Infinite Dimensional Stochastic Analysis
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Author : Zhi-yuan Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang 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 2012-12-06 with Mathematics categories.
The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).
Option Theory With Stochastic Analysis
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Author : Fred Espen Benth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Option Theory With Stochastic Analysis written by Fred Espen Benth 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 2012-12-06 with Business & Economics categories.
This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.
Stochastic Analysis For Poisson Point Processes
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Author : Giovanni Peccati
language : en
Publisher: Springer
Release Date : 2016-07-07
Stochastic Analysis For Poisson Point Processes written by Giovanni Peccati and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-07 with Mathematics categories.
Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.
Stochastic Analysis Of Biochemical Systems
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Author : David F. Anderson
language : en
Publisher: Springer
Release Date : 2015-04-23
Stochastic Analysis Of Biochemical Systems written by David F. Anderson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-23 with Mathematics categories.
This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other areas of science and technology. These notes are based in part on lectures given by Professor Anderson at the University of Wisconsin – Madison and by Professor Kurtz at Goethe University Frankfurt.
Adventures In Stochastic Processes
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Author : Sidney I. Resnick
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Adventures In Stochastic Processes written by Sidney I. Resnick 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 2013-12-11 with Mathematics categories.
Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. In a lively and imaginative presentation, studded with examples, exercises, and applications, and supported by inclusion of computational procedures, the author has created a textbook that provides easy access to this fundamental topic for many students of applied sciences at many levels. With its carefully modularized discussion and crystal clear differentiation between rigorous proof and plausibility argument, it is accessible to beginners but flexible enough to serve as well those who come to the course with strong backgrounds. The prerequisite background for reading the book is a graduate level pre-measure theoretic probability course. No knowledge of measure theory is presumed and advanced notions of conditioning are scrupulously avoided until the later chapters of the book. The tools of applied probability---discrete spaces, Markov chains, renewal theory, point processes, branching processes, random walks, Brownian motion---are presented to the reader in illuminating discussion. Applications include such topics as queuing, storage, risk analysis, genetics, inventory, choice, economics, sociology, and other. Because of the conviction that analysts who build models should know how to build them for each class of process studied, the author has included such constructions.
Stochastic Analysis
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Author : M. T. Barlow
language : en
Publisher: Cambridge University Press
Release Date : 1991-10-25
Stochastic Analysis written by M. T. Barlow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-10-25 with Mathematics categories.
Papers from the Symposium on stochastic analysis, which took place at the University of Durham in July 1990.
Fundamentals Of Stochastic Filtering
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Author : Alan Bain
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-08
Fundamentals Of Stochastic Filtering written by Alan Bain 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 2008-10-08 with Mathematics categories.
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.