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Best probability theory renyi reviews
1. Probability Theory (Dover Books on Mathematics)
Description
The founder of Hungary's Probability Theory School, A. Rnyi made significant contributions to virtually every area of mathematics. This introductory text is the product of his extensive teaching experience and is geared toward readers who wish to learn the basics of probability theory, as well as those who wish to attain a thorough knowledge in the field.
Based on the author's lectures at the University of Budapest, this text requires no preliminary knowledge of probability theory. Readers should, however, be familiar with other branches of mathematics, including a thorough understanding of the elements of the differential and integral calculus and the theory of real and complex functions. These well-chosen problems and exercises illustrate the algebras of events, discrete random variables, characteristic functions, and limit theorems. The text concludes with an extensive appendix that introduces information theory.
Based on the author's lectures at the University of Budapest, this text requires no preliminary knowledge of probability theory. Readers should, however, be familiar with other branches of mathematics, including a thorough understanding of the elements of the differential and integral calculus and the theory of real and complex functions. These well-chosen problems and exercises illustrate the algebras of events, discrete random variables, characteristic functions, and limit theorems. The text concludes with an extensive appendix that introduces information theory.
2. Universal Theory for Strong Limit Theorems of Probability
Description
This is the first book which the universal approach to strong laws of probability is discussed in. The universal theories are described for three important objects of probability theory: sums of independent random variables, processes with independent increments and renewal processes. Further generalizations are mentioned. Besides strong laws, large deviations are of independent interest. The case of infinite variations is considered as well. Readers can examine appropriate techniques and methods. Optimality of conditions is discussed.Readership: Graduate students, researchers in Probability.
3. A Diary on Information Theory (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section)
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Used Book in Good ConditionDescription
This book conveys to the non-specialist some of the deepest ideas in mathematics. The first chapter, On the Mathematical Notion of Information, is a sequel to the author's previous works, Dialogues on Mathematics, and Letters on Probability. Other chapters provide thoughtful discussion of the teaching of probability theory, the diverse and surprising applications of the work of Fibonacci, and a mathematician's battle with the casinos. Provides basic introduction to what mathematics is and how it applies to everyday life.4. Foundations of Probability (Dover Books on Mathematics)
Description
Taking an innovative approach to both content and methods, this book explores the foundations, basic concepts, and fundamental results of probability theory. Geared toward those unfamiliar with probability theory, it offers a firm basis for the study of topics related to the probability of mathematical statistics and to information theory.
The effective construction of probability spaces receives particular attention. Author Alfred Rnyiformer Director of the Mathematical Institute of the Hungarian Academy of Sciences and an expert in the fields of probability theory, mathematical statistics, and number theoryconsidered effective construction of probability spaces particularly important to applying methods and results of probability theory to other branches of mathematics. Professor Rnyi discusses basic theorems of probability theory in terms specific to the theorem in question, rather than in the most general form. His rigorous treatment also covers the mathematical notions of experiments and independence, the laws of chance for independent random variables, and the effects of dependence. Two brief appendixes offer helpful background in measure theory and functional analysis.
The effective construction of probability spaces receives particular attention. Author Alfred Rnyiformer Director of the Mathematical Institute of the Hungarian Academy of Sciences and an expert in the fields of probability theory, mathematical statistics, and number theoryconsidered effective construction of probability spaces particularly important to applying methods and results of probability theory to other branches of mathematics. Professor Rnyi discusses basic theorems of probability theory in terms specific to the theorem in question, rather than in the most general form. His rigorous treatment also covers the mathematical notions of experiments and independence, the laws of chance for independent random variables, and the effects of dependence. Two brief appendixes offer helpful background in measure theory and functional analysis.
5. Information Theoretic Learning: Renyi's Entropy and Kernel Perspectives (Information Science and Statistics)
Description
This book is the first cohesive treatment of ITL algorithms to adapt linear or nonlinear learning machines both in supervised and unsupervised paradigms. It compares the performance of ITL algorithms with the second order counterparts in many applications.6. Large Deviations for Random Graphs: cole d't de Probabilits de Saint-Flour XLV - 2015 (Lecture Notes in Mathematics)
Description
This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.
