Lectures On Probability Theory And Mathematical Statistics 2nd Edition
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Lectures On Probability Theory And Mathematical Statistics 2nd Edition
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Author : Marco Taboga
language : en
Publisher:
Release Date : 2012-12-08
Lectures On Probability Theory And Mathematical Statistics 2nd Edition written by Marco Taboga and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-08 with Mathematical statistics categories.
This book is a collection of lectures on probability theory and mathematical statistics. It provides an accessible introduction to topics that are not usually found in elementary textbooks. It collects results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books.The main topics covered by the book are as follows.PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions.PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions.PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions.PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart.PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions.PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutski's Theorem.PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.
Mathematical Foundations Of Reinforcement Learning
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Author : Shiyu Zhao
language : en
Publisher: Springer Nature
Release Date : 2025-01-21
Mathematical Foundations Of Reinforcement Learning written by Shiyu Zhao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-21 with Computers categories.
This book provides a mathematical yet accessible introduction to the fundamental concepts, core challenges, and classic reinforcement learning algorithms. It aims to help readers understand the theoretical foundations of algorithms, providing insights into their design and functionality. Numerous illustrative examples are included throughout. The mathematical content is carefully structured to ensure readability and approachability. The book is divided into two parts. The first part is on the mathematical foundations of reinforcement learning, covering topics such as the Bellman equation, Bellman optimality equation, and stochastic approximation. The second part explicates reinforcement learning algorithms, including value iteration and policy iteration, Monte Carlo methods, temporal-difference methods, value function methods, policy gradient methods, and actor-critic methods. With its comprehensive scope, the book will appeal to undergraduate and graduate students, post-doctoral researchers, lecturers, industrial researchers, and anyone interested in reinforcement learning.
A Course Of Stochastic Analysis
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Author : Alexander Melnikov
language : en
Publisher: Springer Nature
Release Date : 2023-04-02
A Course Of Stochastic Analysis written by Alexander Melnikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-02 with Mathematics categories.
The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes. The main purpose of the book is to present, in a short and sufficiently self-contained form, the methods and results of the contemporary theory of stochastic analysis and to show how these methods and results work in mathematical finance and statistics of random processes. The book can be considered as a textbook for both senior undergraduate and graduate courses on this subject. The book can be helpful for undergraduate and graduate students, instructors and specialists on stochastic analysis and its applications.
Probability Theory And Mathematical Statistics For Engineers
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Author : V. S. Pugachev
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Probability Theory And Mathematical Statistics For Engineers written by V. S. Pugachev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables. The book underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vectors and their distributions, including conditional distributions of projections of a random vector, conditional numerical characteristics, and information contained in random variables. The book elaborates on the functions of random variables and estimation of parameters of distributions. Topics include frequency as a probability estimate, estimation of statistical characteristics, estimation of the expectation and covariance matrix of a random vector, and testing the hypotheses on the parameters of distributions. The text then takes a look at estimator theory and estimation of distributions. The book is a vital source of data for students, engineers, postgraduates of applied mathematics, and other institutes of higher technical education.
Probability Theory
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Author : Heinz Bauer
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-03
Probability Theory written by Heinz Bauer 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 2011-05-03 with Mathematics categories.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Modern Discrete Probability
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Author : Sébastien Roch
language : en
Publisher: Cambridge University Press
Release Date : 2024-01-18
Modern Discrete Probability written by Sébastien Roch 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 2024-01-18 with Mathematics categories.
Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering.
Pseudo Differential Operators Markov Processes
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Author : Niels Jacob
language : en
Publisher: Imperial College Press
Release Date : 2005
Pseudo Differential Operators Markov Processes written by Niels Jacob and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further developed and applications are discussed. Due to the non-locality of the generators, the processes are jump processes and their relations to Levy processes are investigated. Special emphasis is given to the symbol of a process, a notion which generalizes that of the characteristic exponent of a Levy process and provides a natural link to pseudo-differential operator theory.
Pseudo Differential Operators And Markov Processes Volume Iii Markov Processes And Applications
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Author : Niels Jacob
language : en
Publisher: World Scientific
Release Date : 2005-06-14
Pseudo Differential Operators And Markov Processes Volume Iii Markov Processes And Applications written by Niels Jacob and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-14 with Mathematics categories.
This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further developed and applications are discussed. Due to the non-locality of the generators, the processes are jump processes and their relations to Levy processes are investigated. Special emphasis is given to the symbol of a process, a notion which generalizes that of the characteristic exponent of a Levy process and provides a natural link to pseudo-differential operator theory./a
Mathematical Statistics
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Author : Thomas S. Ferguson
language : en
Publisher: Academic Press
Release Date : 2014-07-10
Mathematical Statistics written by Thomas S. Ferguson 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.
Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in mathematics.
Convergence Of Stochastic Processes
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Author : D. Pollard
language : en
Publisher: David Pollard
Release Date : 1984-10-08
Convergence Of Stochastic Processes written by D. Pollard and has been published by David Pollard this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-10-08 with Mathematics categories.
Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.