Symmetric Markov Processes Time Change And Boundary Theory Lms 35
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Symmetric Markov Processes Time Change And Boundary Theory Lms 35
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Author : Zhen-Qing Chen
language : en
Publisher: Princeton University Press
Release Date : 2012
Symmetric Markov Processes Time Change And Boundary Theory Lms 35 written by Zhen-Qing Chen and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.
40 2 158
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Author : 中央研究院數學研究所
language : zh-CN
Publisher: 中央研究院數學研究所
Release Date : 2016-05-04
40 2 158 written by 中央研究院數學研究所 and has been published by 中央研究院數學研究所 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-04 with Mathematics categories.
本期「有朋自遠方來」訪談馬志明教授。馬教授是中國國家科學院士，對機率論及隨機分析有卓越的貢獻。他在求學時期遭逢文革，自學出身，在匱乏的環境，力學不輟，打下扎實且廣博的數學基礎。二十七歲進大學時，數學程度已遠高於諸多教授。研究所時期，開始深耕機率論領域。訪問德國期間，與歐洲學者合作，獲得狄氏型(Dirichlet form)及馬氏過程( Markov process)對應關係的突破性進展。一枝草，一點露；當年那個偏鄉弱勢孩子，無依無恃，但質樸厚實、生氣盎然，如同瓜苗沾雨露、承地氣而一路成長茁壯、開花結果。 訪談中，馬教授精簡地介紹了狄氏型及相關工作，清晰陳述問題背景、研究成果。近年來馬教授涉足統計、生物、資訊科學，成就多元，各有精采。以此背景，他論及數學與統計學的競合，期許雙方有胸襟氣度互相欣賞。他也不吝給予年輕學子建議，鼓勵自學，博學多聞，繼而將知識融為一體、化為無形。對目前急功近利的學術氛圍，他提出批評與建言，鞭辟入裡。 承前兩期，本期繼續轉載David Tong教授之廣義相對論講稿，內文淺顯闡述愛因斯坦方程式 (Einstein field equations)表達的概念。與此相對照，張海潮、莊正良教授考慮行星繞日的橢圓軌道，計算橢圓曲率，藉此推導牛頓力學的基石：萬有引力平方反比定律。 周伯新先生提出算幾不等式的視覺化證明，巧妙地將幾何平均等同為某平行四邊形的面積。王九逵、胡門昌、張清煇教授延續155期的工作，重排交錯數列，使其部分和數列之上下極限符合指定數值。吳波先生探討一族圓內接四邊形，其邊長與面積皆為有理數，並借助初等數論具體構造出如此之四邊形。 明代王文素《算學寶鑒》繪有六種幻圖，將連續自然數在不同約束條件下適當配置，可視為組合學的區組設計( block design )問題。羅文素教授重繪這些圖，並特別處理「三同六變」圖文，將之歸結為三類子問題。他也列舉了其他推廣類型的問題，讀者不妨嘗試解題。 兩玩家賭博，初始分別有m及n元，每一回合賭注一元，大概幾回合後某一位玩家的錢將輸光?楊大緯先生以電腦模擬 106 局，推估約 mn 回合後某玩家將分文不剩，繼而以數學嚴謹證明此猜測之正確性。楊先生藉此示範電腦於數學研究之大用。與此略相關，話說日前人機對弈，AphaGo人工智慧系統與九段圍棋高手對陣五局，四勝一負，震撼世人。讀者想必也因此重新思考了數學、電腦、教育的相互關係，試圖釐清數學教育及數學家的價值、意義、不可取代性。歡迎讀者投稿，從各個角度深入探討相關議題。 梁惠禎 2016年6月
Partially Observed Markov Decision Processes
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Author : Vikram Krishnamurthy
language : en
Publisher: Cambridge University Press
Release Date : 2016-03-21
Partially Observed Markov Decision Processes written by Vikram Krishnamurthy 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 2016-03-21 with Mathematics categories.
This book covers formulation, algorithms, and structural results of partially observed Markov decision processes, whilst linking theory to real-world applications in controlled sensing. Computations are kept to a minimum, enabling students and researchers in engineering, operations research, and economics to understand the methods and determine the structure of their optimal solution.
Theory Of Markov Processes
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Author : Evgeniĭ Borisovich Dynkin
language : en
Publisher: Courier Corporation
Release Date : 2006-01-01
Theory Of Markov Processes written by Evgeniĭ Borisovich Dynkin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Mathematics categories.
An investigation of the logical foundations of the theory behind Markov random processes, this text explores subprocesses, transition functions, and conditions for boundedness and continuity. Rather than focusing on probability measures individually, the work explores connections between functions. An elementary grasp of the theory of Markov processes is assumed. Starting with a brief survey of relevant concepts and theorems from measure theory, the text investigates operations that permit an inspection of the class of Markov processes corresponding to a given transition function. It advances to the more complicated operations of generating a subprocess, followed by examinations of the construction of Markov processes with given transition functions, the concept of a strictly "Markov process," and the conditions required for boundedness and continuity of a Markov process. Addenda, notes, references, and indexes supplement the text.
Reinforcement Learning
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Author : Richard S. Sutton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Reinforcement Learning written by Richard S. Sutton 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 Computers categories.
Reinforcement learning is the learning of a mapping from situations to actions so as to maximize a scalar reward or reinforcement signal. The learner is not told which action to take, as in most forms of machine learning, but instead must discover which actions yield the highest reward by trying them. In the most interesting and challenging cases, actions may affect not only the immediate reward, but also the next situation, and through that all subsequent rewards. These two characteristics -- trial-and-error search and delayed reward -- are the most important distinguishing features of reinforcement learning. Reinforcement learning is both a new and a very old topic in AI. The term appears to have been coined by Minsk (1961), and independently in control theory by Walz and Fu (1965). The earliest machine learning research now viewed as directly relevant was Samuel's (1959) checker player, which used temporal-difference learning to manage delayed reward much as it is used today. Of course learning and reinforcement have been studied in psychology for almost a century, and that work has had a very strong impact on the AI/engineering work. One could in fact consider all of reinforcement learning to be simply the reverse engineering of certain psychological learning processes (e.g. operant conditioning and secondary reinforcement). Reinforcement Learning is an edited volume of original research, comprising seven invited contributions by leading researchers.
Dirichlet Forms And Symmetric Markov Processes
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Author : Masatoshi Fukushima
language : en
Publisher: Walter de Gruyter
Release Date : 2011
Dirichlet Forms And Symmetric Markov Processes written by Masatoshi Fukushima and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edition, the authors not only revise
Analysis Of Heat Equations On Domains Lms 31
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Author : El-Maati Ouhabaz
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
Analysis Of Heat Equations On Domains Lms 31 written by El-Maati Ouhabaz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Mathematics categories.
This is the first comprehensive reference published on heat equations associated with non self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats Lp properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory and mathematical physics. This book addresses new developments and applications of Gaussian upper bounds to spectral theory. In particular, it shows how such bounds can be used in order to prove Lp estimates for heat, Schrödinger, and wave type equations. A significant part of the results have been proved during the last decade. The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second order elliptic operators in divergence form, heat kernel bounds, and their applications. It will also be of value to mathematical physicists. The author supplies readers with several references for the few standard results that are stated without proofs.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Lectures On Optimal Transport
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Author : Luigi Ambrosio
language : en
Publisher: Springer Nature
Release Date : 2021-07-22
Lectures On Optimal Transport written by Luigi Ambrosio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-22 with Mathematics categories.
This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.
Log Gases And Random Matrices Lms 34
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Author : Peter J. Forrester
language : en
Publisher: Princeton University Press
Release Date : 2010-07-01
Log Gases And Random Matrices Lms 34 written by Peter J. Forrester and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.
Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.