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1. Probability Theory II (Graduate Texts in Mathematics)
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Probability Theory IIDescription
This book is intended as a text for graduate students and as a reference for workers in probability and statistics. The prerequisite is honest calculus. The material covered in Parts Two to Five inclusive requires about three to four semesters of graduate study. The introductory part may serve as a text for an undergraduate course in elementary probability theory. Numerous historical marks about results, methods, and the evolution of various fields are an intrinsic part of the text. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated.2. Probability Theory II (Graduate Texts in Mathematics) by M. Loeve (1994-08-12)
3. Probability Theory I, 4th Edition (v. 1)
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Probability Theory IDescription
This fourth edition contains several additions. The main ones con cern three closely related topics: Brownian motion, functional limit distributions, and random walks. Besides the power and ingenuity of their methods and the depth and beauty of their results, their importance is fast growing in Analysis as well as in theoretical and applied Proba bility. These additions increased the book to an unwieldy size and it had to be split into two volumes. About half of the first volume is devoted to an elementary introduc tion, then to mathematical foundations and basic probability concepts and tools. The second half is devoted to a detailed study of Independ ence which played and continues to playa central role both by itself and as a catalyst. The main additions consist of a section on convergence of probabilities on metric spaces and a chapter whose first section on domains of attrac tion completes the study of the Central limit problem, while the second one is devoted to random walks. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated. The main addition consists of a chapter on Brownian motion and limit distributions.4. Probability Theory: Third Edition (Dover Books on Mathematics)
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"This is a very scholarly book in the best tradition of analysis. Nothing else of this type exists for the benefit of the serious student of the subject and it is safe to predict that it will remain a standard compendium for many years to come." S. Vajda in Zentralblatt fr Mathematik
In the decades following its 1963 publication, this volume served as the standard advanced text in probability theory. Geared toward graduate students and professionals in the field of probability and statistics, the treatment offers extensive introductory material and is suitable for an undergraduate course in probability theory. The first four chapters cover notions of measure theory plus general concepts and tools of probability theory. Subsequent chapters explore sums of independent random variables, the central limit problem, conditioning, independence and dependence, ergodic theorems, and second order properties. The final two chapters examine foundations, martingales, and decomposability as well as Markov processes.
5. Probability Theory: University Series in Higher Mathematics
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Probability Theory University Series in Higher MathematicsDescription
Format Paperback Subject Literary Collections6. Stochastic Dynamics of Structures
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Stochastic Dynamics of StructuresDescription
In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures within the innovative theoretical framework of physical stochastic systems. The authors outline the fundamental concepts of random variables, stochastic process and random field, and orthogonal expansion of random functions. Readers will gain insight into core concepts such as stochastic process models for typical dynamic excitations of structures, stochastic finite element, and random vibration analysis. Li and Chen also cover advanced topics, including the theory of and elaborate numerical methods for probability density evolution analysis of stochastic dynamical systems, reliability-based design, and performance control of structures.Stochastic Dynamics of Structures presents techniques for researchers and graduate students in a wide variety of engineering fields: civil engineering, mechanical engineering, aerospace and aeronautics, marine and offshore engineering, ship engineering, and applied mechanics. Practicing engineers will benefit from the concise review of random vibration theory and the new methods introduced in the later chapters.
"The book is a valuable contribution to the continuing development of the field of stochastic structural dynamics, including the recent discoveries and developments by the authors of the probability density evolution method (PDEM) and its applications to the assessment of the dynamic reliability and control of complex structures through the equivalent extreme-value distribution."
A. H-S. Ang, NAE, Hon. Mem. ASCE, Research Professor, University of California, Irvine, USA
"The authors have made a concerted effort to present a responsible and even holistic account of modern stochastic dynamics. Beyond the traditional concepts, they also discuss theoretical tools of recent currency such as the Karhunen-Loeve expansion, evolutionary power spectra, etc. The theoretical developments are properly supplemented by examples from earthquake, wind, and ocean engineering. The book is integrated by also comprising several useful appendices, and an exhaustive list of references; it will be an indispensable tool for students, researchers, and practitioners endeavoring in its thematic field."
Pol Spanos, NAE, Ryon Chair in Engineering, Rice University, Houston, USA
7. Probability Theory I: 1 (Graduate Texts in Mathematics) by M. Loeve (22-Jun-2012) Paperback