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A Little Book of Martingales
This concise textbook, fashioned along the syllabus for master's and Ph.D. programmes, covers basic results on discrete-time martingales and applications. It includes additional interesting and useful topics, providing the ability to move beyond. Adequate details are provided with exercises within the text and at the end of chapters. Basic results include Doob's optional sampling theorem, Wald identities, Doob's maximal inequality, upcrossing lemma, time-reversed martingales, a variety of convergence results and a limited discussion of the Burkholder inequalities. Applications include the 0-1 laws of Kolmogorov and Hewitt-Savage, the strong laws for U-statistics and exchangeable sequences, De Finetti's theorem for exchangeable sequences and Kakutani's theorem for product martingales. A simple central limit theorem for martingales is proven and applied to a basic urn model, the trace of a random matrix and Markov chains. Additional topics include forward martingale representation for U-statistics, conditional Borel-Cantelli lemma, Azuma-Hoeffding inequality, conditional three series theorem, strong law for martingales and the Kesten-Stigum theorem for a simple branching process. The prerequisite for this course is a first course in measure theoretic probability. The book recollects its essential concepts and results, mostly without proof, but full details have been provided for the Radon-Nikodym theorem and the concept of conditional expectation.
€ 53,49 -
Elements of Measure and Probability
€ 71,50 -
A Little Book of Martingales
€ 76,95 -
Ethnomathematics and Mathematics Education
International Perspectives in Times of Local and Global ChangeIn this edited book, the authors explore how ethnomathematics supports transformation of educational systems toward regaining cultural reclamation and self-confidence, challenges colonial logics for decolonizing and Indigenizing mathematics education, and engages with actions for critical and social justice issues.
€ 219,95 -
Random Matrices and Non-Commutative Probability
Free Probability/Non-commutative Probability has gained much attentionsignificant advances have been made since its initiation in the 1990’s. Though it started as a branch of Mathematics, it has found significant applications in statistics, wireless communication etc, particularly through deep and interesting connections with Random Matrix Theory.
€ 85,95 -
Fun with mathematics
€ 20,95 -
Mobile Platforms and Development Environments
Table of Contents: From the Newton to the iPhone / iOS / Android / Windows Phone / Mobile Web / Platform-in-Platform: Location-Based Services (LBS) / The Future of Mobile Platforms / TwitterSearch Sample Application
€ 32,95 -
Random Matrices and Non-Commutative Probability
Free Probability/Non-commutative Probability has gained much attentionsignificant advances have been made since its initiation in the 1990’s. Though it started as a branch of Mathematics, it has found significant applications in statistics, wireless communication etc, particularly through deep and interesting connections with Random Matrix Theory.
€ 235,95 -
Mathematics Formulae for School Students
Clear Your Basic Concepts to Solve Problems Quickly€ 16,50 -
Patterned Random Matrices
This book focuses on the limit spectral distribution (LSD) of patterned random matrices and provides a comprehensive variety of LSD results. It is accessible to first or second years Master's students and uses very elementary techniques. It is suitable for a beginner in random matrices with some probability background.
€ 70,50 -
Large Covariance and Autocovariance Matrices
The material will be based on very recent advances in the theory and application of large covariance and autocovariance matrices. Technologies and methods in medical sciences, image processing, and other fields generate data where the dimension is large compared to the sample size and may also increase as the next set of measurements become avai
€ 70,50 -
Random Circulant Matrices
This book is on properties of the eigenvalues of several different Random Circulant- type matrices as the dimension goes to infinity. In particular, we consider the bulk behavior of the eigenvalues (limiting spectral distribution) and also the edge behavior of the eigenvalues.
€ 70,50