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Stochastic Analysis and Random Maps in Hilbert Space

Stochastic Analysis and Random Maps in Hilbert Space
Author: A. A. Dorogovtsev
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 116
Release: 2019-01-14
Genre: Mathematics
ISBN: 3110618141

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This book is devoted to stochastic operators in Hilbert space. A number of models in modern probability theory apply the notion of a stochastic operator in explicit or latent form. In this book, objects from the Gaussian case are considered. Therefore, it is useful to consider all random variables and elements as functionals from the Wiener process or its formal derivative, i.e. white noise. The book consists of five chapters. The first chapter is devoted to stochastic calculus and its main goal is to prepare the tools for solving stochastic equations. In the second chapter the structure of stochastic equations, mainly the structure of Gaussian strong linear operators, is studied. In chapter 3 the definition of the action of the stochastic operator on random elements in considered. Chapter 4 deals with the mathematical models in which the notions of stochastic calculus arise and in the final chapter the equation with random operators is considered.


Stochastic Analysis for Gaussian Random Processes and Fields

Stochastic Analysis for Gaussian Random Processes and Fields
Author: Vidyadhar S. Mandrekar
Publisher: CRC Press
Total Pages: 200
Release: 2015-06-23
Genre: Mathematics
ISBN: 1498707823

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Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs).The book begins with preliminary results on covariance and associated RKHS


Real And Stochastic Analysis: Current Trends

Real And Stochastic Analysis: Current Trends
Author: Malempati Madhusudana Rao
Publisher: World Scientific
Total Pages: 576
Release: 2013-11-26
Genre: Mathematics
ISBN: 9814551295

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This book presents the current status and research trends in Stochastic Analysis. Several new and emerging research areas are described in detail, highlighting the present outlook in Stochastic Analysis and its impact on abstract analysis. The book focuses on treating problems in areas that serve as a launching pad for continual research.


Hilbert Space Methods in Probability and Statistical Inference

Hilbert Space Methods in Probability and Statistical Inference
Author: Christopher G. Small
Publisher: John Wiley & Sons
Total Pages: 268
Release: 2011-09-15
Genre: Mathematics
ISBN: 1118165535

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Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.


Stochastic Analysis

Stochastic Analysis
Author: Paul Malliavin
Publisher: Springer
Total Pages: 346
Release: 2002-04-01
Genre: Mathematics
ISBN: 3540570241

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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.


Gaussian Hilbert Spaces

Gaussian Hilbert Spaces
Author: Svante Janson
Publisher: Cambridge University Press
Total Pages: 358
Release: 1997-06-12
Genre: Mathematics
ISBN: 0521561280

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This book treats the very special and fundamental mathematical properties that hold for a family of Gaussian (or normal) random variables. Such random variables have many applications in probability theory, other parts of mathematics, statistics and theoretical physics. The emphasis throughout this book is on the mathematical structures common to all these applications. This will be an excellent resource for all researchers whose work involves random variables.


Stochastics in Finite and Infinite Dimensions

Stochastics in Finite and Infinite Dimensions
Author: Takeyuki Hida
Publisher: Springer Science & Business Media
Total Pages: 436
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461201675

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During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong.


Infinite Dimensional Stochastic Analysis: In Honor Of Hui-hsiung Kuo

Infinite Dimensional Stochastic Analysis: In Honor Of Hui-hsiung Kuo
Author: Ambar N Sengupta
Publisher: World Scientific
Total Pages: 257
Release: 2008-02-25
Genre: Mathematics
ISBN: 9814472239

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This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.


Stochastic Partial Differential Equations with Lévy Noise

Stochastic Partial Differential Equations with Lévy Noise
Author: S. Peszat
Publisher: Cambridge University Press
Total Pages: 45
Release: 2007-10-11
Genre: Mathematics
ISBN: 0521879892

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Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.


Stochastic Analysis And Applications: Proceedings Of The Fifth Gregynog Symposium

Stochastic Analysis And Applications: Proceedings Of The Fifth Gregynog Symposium
Author: Ian M Davies
Publisher: World Scientific
Total Pages: 522
Release: 1996-03-20
Genre:
ISBN: 9814548111

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This volume contains papers which were presented at a meeting entitled “Stochastic Analysis and Applications“ held at Gregynog Hall, Powys, from the 9th — 14th July 1995. The meeting consisted of a mixture of plenary/review talks and special interest sessions covering most of the current areas of activity in stochastic analysis. The meeting was jointly organized by the Department of Mathematics, University of Wales Swansea and the Mathematics Institute, University of Warwick in connection with the Stochastic Analysis year of activity. The papers contained herein are accessible to workers in the field of stochastic analysis and give a good coverage of topics of current interest in the research community.