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- Cambridge Studies in Advanced Mathematics
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- A note on the self-similar solutions to the spontaneous fragmentation equation.
Mouthon et al. Doumic and P. Escobedo, S. Mischler, and M. Fredrickson, D. Ramkrishna, and H. Tsuchiya , Statistics and dynamics of procaryotic cell populations , Mathematical Biosciences , vol. Haas , Loss of mass in deterministic and random fragmentations , Stochastic Processes and their Applications , pp. Haas , Asymptotic behavior of solutions of the fragmentation equation with shattering: An approach via self-similar Markov processes , The Annals of Applied Probability , vol.
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Hewitt and K. Stromberg , Real and Abstract Analysis. Mischler and J. Scher , Spectral analysis of semigroups and growth-fragmentation equations. Robert, M.
Series: Cambridge studies in advanced mathematics
Hoffmann, N. Consequently, a course in probability and random processes is a prerequisite for further study in communications or signal processing. Gubner presents a primary text that progresses from advanced undergraduate level, assuming a modest knowledge of probability, through to the more complex topics suitable for graduates, including random vectors, Gaussian random vectors, random processes and Markov chains. Describing tools and results that are used extensively in the field, this is more than a textbook: it is also a valuable reference for researchers working in communications, signal processing, and computer network traffic analysis.
With chapter outlines, over worked examples, some problems and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Introduction to probability; 2. Introduction to discrete random variables; 3.
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More about discrete random variables; 4. Continuous random variables; 5. Cumulative distribution functions and their applications; 6. Statistics; 7. Bivariate random variables; 8.
Cambridge Studies in Advanced Mathematics
Introduction to random vectors; 9. Gaussian random vectors; Introduction to random processes; Advanced concepts in random processes; Introduction to Markov chains; Mean convergence and applications; Other modes of convergence; Self similarity and long-range dependence; Bibliography; Index. This book, by the author of the acclaimed Levy Processes, is the first comprehensive theoretical account of mathematical models for situations where either phenomenon occurs randomly and repeatedly as time passes. This self-contained treatment develops the models in a way that makes recent developments in the field accessible.
Written for readers with a solid background in probability, its careful exposition allows graduate students, as well as working mathematicians, to approach the material with confidence. Self-similar fragmentation chains; 2. Random partitions; 3.
Exchangeable fragmentations; 4. Exchangeable coalescents; 5. Asymptotic regimes in stochastic coalescence; References; List of symbols; Index.
Since its emergence in the s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering.
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This book is the first to give a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course on an advanced undergraduate or beginning graduate level , and is also well-suited for the individual study of free probability.
Basic Concepts: 1. Non-commutative probability spaces and distributions; 2. A case study of non-normal distribution; 3. Non-commutative joint distributions; 5. Definition and basic properties of free independence; 6.