Asymptotic Properties Of Permanental Sequences
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Author | : Michael B. Marcus |
Publisher | : Springer Nature |
Total Pages | : 114 |
Release | : 2021-03-30 |
Genre | : Mathematics |
ISBN | : 3030694852 |
This SpringerBriefs employs a novel approach to obtain the precise asymptotic behavior at infinity of a large class of permanental sequences related to birth and death processes and autoregressive Gaussian sequences using techniques from the theory of Gaussian processes and Markov chains. The authors study alpha-permanental processes that are positive infinitely divisible processes determined by the potential density of a transient Markov process. When the Markov process is symmetric, a 1/2-permanental process is the square of a Gaussian process. Permanental processes are related by the Dynkin isomorphism theorem to the total accumulated local time of the Markov process when the potential density is symmetric, and by a generalization of the Dynkin theorem by Eisenbaum and Kaspi without requiring symmetry. Permanental processes are also related to chi square processes and loop soups. The book appeals to researchers and advanced graduate students interested in stochastic processes, infinitely divisible processes and Markov chains.
Author | : Alexander Melnikov |
Publisher | : Springer Nature |
Total Pages | : 214 |
Release | : 2023-04-02 |
Genre | : Mathematics |
ISBN | : 3031253264 |
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.
Author | : Grzegorz Rempala |
Publisher | : Springer Science & Business Media |
Total Pages | : 192 |
Release | : 2007-12-06 |
Genre | : Mathematics |
ISBN | : 0387751467 |
This superb explication of a complex subject presents the current state of the art of the mathematical theory of symmetric functionals on random matrices. It emphasizes its connection with the statistical non-parametric estimation theory. The book provides a detailed description of the approach of symmetric function decompositions to the asymptotic theory of symmetric functionals, including the classical theory of U-statistics. It also presents applications of the theory.
Author | : American Mathematical Society |
Publisher | : |
Total Pages | : 540 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 866 |
Release | : 1990 |
Genre | : Physics |
ISBN | : |
Author | : Vladimir S. Korolyuk |
Publisher | : Springer Science & Business Media |
Total Pages | : 558 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401735158 |
The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.
Author | : Jerome Adda |
Publisher | : MIT Press |
Total Pages | : 297 |
Release | : 2023-05-09 |
Genre | : Business & Economics |
ISBN | : 0262547880 |
An integrated approach to the empirical application of dynamic optimization programming models, for students and researchers. This book is an effective, concise text for students and researchers that combines the tools of dynamic programming with numerical techniques and simulation-based econometric methods. Doing so, it bridges the traditional gap between theoretical and empirical research and offers an integrated framework for studying applied problems in macroeconomics and microeconomics. In part I the authors first review the formal theory of dynamic optimization; they then present the numerical tools and econometric techniques necessary to evaluate the theoretical models. In language accessible to a reader with a limited background in econometrics, they explain most of the methods used in applied dynamic research today, from the estimation of probability in a coin flip to a complicated nonlinear stochastic structural model. These econometric techniques provide the final link between the dynamic programming problem and data. Part II is devoted to the application of dynamic programming to specific areas of applied economics, including the study of business cycles, consumption, and investment behavior. In each instance the authors present the specific optimization problem as a dynamic programming problem, characterize the optimal policy functions, estimate the parameters, and use models for policy evaluation. The original contribution of Dynamic Economics: Quantitative Methods and Applications lies in the integrated approach to the empirical application of dynamic optimization programming models. This integration shows that empirical applications actually complement the underlying theory of optimization, while dynamic programming problems provide needed structure for estimation and policy evaluation.
Author | : T. Kohonen |
Publisher | : Springer Science & Business Media |
Total Pages | : 188 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642963846 |
About the Scope of This Text This book contains two types of material ~ first, the many divergent and often diffuse meanings given to the concepts of association, associative memory, and associative recaZZ are expounded. A review of this kind was felt necessary because there apparently does not exist any single monograph which could serve as a reference to these topics. But the presentation of the main body of this text is motivated by quite other reasons: in recent years, plenty of interesting mathematical and system-theoretical material has been published which makes it possible to gain a view of associative memory which is different from the conventional abstract and computationally oriented approaches. It seems that the basic operation of associative memory, the storage of information together with the relations or links between the data items, and the selective recall of stored information relative to a piece of key or cue information presented, is not restricted to certain computer-technological implementations but can also be reflected in more general mathematically describable processes in certain physical or other systems, especially in their adaptive state changes. It further seems that some generally known forms of associative memory, namely, certain computer technological artifacts, or abstract systems of concepts or data, are in fact special representations of a class of processes characterized as associative memory.
Author | : Jean-Pierre Aubin |
Publisher | : Springer Science & Business Media |
Total Pages | : 812 |
Release | : 2011-07-13 |
Genre | : Science |
ISBN | : 3642166849 |
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and illustrating them with numerous numerical examples taken from various fields.
Author | : |
Publisher | : |
Total Pages | : 958 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : |