Quantum Stochastics

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Quantum Stochastics And Information

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Author : V. P. Belavkin
language : en
Publisher: World Scientific
Release Date : 2008

Quantum Stochastics And Information written by V. P. Belavkin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.

Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems.This volume contains a selection of regular research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.

Quantum Stochastics

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Author : Mou-Hsiung Chang
language : en
Publisher: Cambridge University Press
Release Date : 2015-02-19

Quantum Stochastics written by Mou-Hsiung Chang 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 2015-02-19 with Language Arts & Disciplines categories.

This book provides a systematic, self-contained treatment of the theory of quantum probability and quantum Markov processes for graduate students and researchers. Building a framework that parallels the development of classical probability, it aims to help readers up the steep learning curve of the quantum theory.

An Introduction To Quantum Stochastic Calculus

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Author : K.R. Parthasarathy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-13

An Introduction To Quantum Stochastic Calculus written by K.R. Parthasarathy 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 2012-12-13 with Mathematics categories.

An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito’s correction formulae for Brownian motion and the Poisson process can be traced to commutation relations or, equivalently, the uncertainty principle. Quantum stochastic integration enables the possibility of seeing new relationships between fermion and boson fields. Many quantum dynamical semigroups as well as classical Markov semigroups are realised through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level. - - - This is an excellent volume which will be a valuable companion both to those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students. (Mathematical Reviews) This monograph gives a systematic and self-contained introduction to the Fock space quantum stochastic calculus in its basic form (...) by making emphasis on the mathematical aspects of quantum formalism and its connections with classical probability and by extensive presentation of carefully selected functional analytic material. This makes the book very convenient for a reader with the probability-theoretic orientation, wishing to make acquaintance with wonders of the noncommutative probability, and, more specifcally, for a mathematics student studying this field. (Zentralblatt MATH) Elegantly written, with obvious appreciation for fine points of higher mathematics (...) most notable is [the] author's effort to weave classical probability theory into [a] quantum framework. (The American Mathematical Monthly)

Stochastics Control And Robotics

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Author : Harish Parthasarathy
language : en
Publisher: CRC Press
Release Date : 2021-06-24

Stochastics Control And Robotics written by Harish Parthasarathy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.

This book discusses various problems in stochastic Processes, Control Theory, Electromagnetics, Classical and Quantum Field Theory & Quantum Stochastics. The problems are chosen to motivate the interested reader to learn more about these subjects from other standard sources. Stochastic Process theory is applied to the study of differential equations of mechanics subject to external noise. Some issues in general relativity like Geodesic motion, field theory in curved space time etc. are discussed via isolated problems. The more recent quantum stochastic process theory as formulated by R.L. Hudson and K. R. Parathasarathy is discussed. This provides a non commutative operator theoretic version of stochastic process theory. V.P. Belavkin's approach to quantum filtering based on non demolition measurements and Hudson Parathasarathy calculus has been discussed in detail. Quantum versions of the simple exclusion model in Markov process theory have been included. 3D Robots carring a current density interacting with an external Klein- Gordon or Electromagnetic field has been given some attention. The readers will after going through this book, be ready to carry out independent research in classical and quantum field theory and stochastic processes as applied to practical problems. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

Stochastics Control And Robotics

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Author : Harish Parthasarathy
language : en
Publisher:
Release Date : 2021

Stochastics Control And Robotics written by Harish Parthasarathy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Control theory categories.

This book discusses various problems in stochastic Processes, Control Theory, Electromagnetics, Classical and Quantum Field Theory & Quantum Stochastics. Note: T& F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

Stochastics In Finite And Infinite Dimensions

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Author : Takeyuki Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stochastics In Finite And Infinite Dimensions written by Takeyuki Hida 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.

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.

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).

Infinite Dimensional Stochastic Analysis

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Author : Hui-Hsiung Kuo
language : en
Publisher: World Scientific
Release Date : 2008

Infinite Dimensional Stochastic Analysis written by Hui-Hsiung Kuo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.

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 Processes In Physics And Chemistry

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Author : N.G. Van Kampen
language : en
Publisher: Elsevier
Release Date : 1992-11-20

Stochastic Processes In Physics And Chemistry written by N.G. Van Kampen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-20 with Science categories.

This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.

Stochastic Partial Differential Equations

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Author : Alison Etheridge
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-13

Stochastic Partial Differential Equations written by Alison Etheridge 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 1995-07-13 with Mathematics categories.

Consists of papers given at the ICMS meeting held in 1994 on this topic, and brings together some of the world's best known authorities on stochastic partial differential equations.