Statistics Of Random Processes Ii

Author by : Robert S. Liptser
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 56
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Description : "Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW


Statistics Of Random Processes I

Author by : R.S. Liptser
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 61
Total Download : 829
File Size : 44,5 Mb
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Description : A considerable number of problems in the statistics of random processes are formulated within the following scheme. On a certain probability space (Q, ff, P) a partially observable random process (lJ,~) = (lJ ~/), t :;::-: 0, is given with only the second component n ~ = (~/), t:;::-: 0, observed. At any time t it is required, based on ~h = g., ° s sst}, to estimate the unobservable state lJ/. This problem of estimating (in other words, the filtering problem) 0/ from ~h will be discussed in this book. It is well known that if M(lJ;)


Statistics And Control Of Random Processes

Author by : A. A. Novikov
Language : en
Publisher by : American Mathematical Soc.
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Total Read : 41
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File Size : 48,5 Mb
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Description : This book contains papers by participants in two seminars, one on Martingales and Statistics of Stochastic Processes, and one on Sequential Analysis, both of which are held at the Steklov Institute of the Russian Academy of Sciences. The papers develop the concepts of martingales and semimartingales and stochastic calculus for them, as well as their applications in statistics and control of stochastic processes. The class of semimartingales--that is, the class of all processes which can be represented as a sum of a martingale and a process with bounded variation--is rather large. It contains such important processes as Brownian motion, Poisson processes, solutions of stochastic differential equations, and others. The papers treat theoretical aspects of statistics of stochastic processes as well as specific models of stochastic processes from the standpoint of their statistics and control. The collection is intended for undergraduate and graduate students and resarchers in probability theory and mathematical statistics.


Statistics Of Random Processes

Author by : Robert S. Liptser
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 20
Total Download : 315
File Size : 54,5 Mb
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Description : The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The required mathematical background is presented in the first volume: the theory of martingales, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic calculus for counting processes. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.


Statistics Of Random Processes

Author by : Robert S. Liptser
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 15
Total Download : 333
File Size : 51,9 Mb
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Description : The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The required mathematical background is presented in the first volume: the theory of martingales, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic calculus for counting processes. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.


Statistics Of Random Processes Ii

Author by : R.S. Liptser
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 9
Total Download : 954
File Size : 53,9 Mb
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Description :


Statistics Of Random Processes I

Author by : R.S. Liptser
Language : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 12
Total Download : 768
File Size : 44,5 Mb
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Description : A considerable number of problems in the statistics of random processes are formulated within the following scheme. On a certain probability space (Q, ff, P) a partially observable random process (lJ,~) = (lJ ~/), t :;::-: 0, is given with only the second component n ~ = (~/), t:;::-: 0, observed. At any time t it is required, based on ~h = g., ° s sst}, to estimate the unobservable state lJ/. This problem of estimating (in other words, the filtering problem) 0/ from ~h will be discussed in this book. It is well known that if M(lJ;)


Statistics Of Random Processes

Author by : Robert Shevilevich Lipt︠s︡er
Language : en
Publisher by : Springer Verlag
Format Available : PDF, ePub, Mobi
Total Read : 37
Total Download : 262
File Size : 47,6 Mb
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Description :


Probability Theory Random Processes And Mathematical Statistics

Author by : Y. Rozanov
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 95
Total Download : 208
File Size : 42,9 Mb
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Description : Probability Theory, Theory of Random Processes and Mathematical Statistics are important areas of modern mathematics and its applications. They develop rigorous models for a proper treatment for various 'random' phenomena which we encounter in the real world. They provide us with numerous tools for an analysis, prediction and, ultimately, control of random phenomena. Statistics itself helps with choice of a proper mathematical model (e.g., by estimation of unknown parameters) on the basis of statistical data collected by observations. This volume is intended to be a concise textbook for a graduate level course, with carefully selected topics representing the most important areas of modern Probability, Random Processes and Statistics. The first part (Ch. 1-3) can serve as a self-contained, elementary introduction to Probability, Random Processes and Statistics. It contains a number of relatively sim ple and typical examples of random phenomena which allow a natural introduction of general structures and methods. Only knowledge of elements of real/complex analysis, linear algebra and ordinary differential equations is required here. The second part (Ch. 4-6) provides a foundation of Stochastic Analysis, gives information on basic models of random processes and tools to study them. Here a familiarity with elements of functional analysis is necessary. Our intention to make this course fast-moving made it necessary to present important material in a form of examples.


Statistics And Control Of Stochastic Processes The Liptser Festschrift

Author by : Kabanov Yu M
Language : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 88
Total Download : 308
File Size : 47,5 Mb
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Description : This volume contains papers presented at the Steklov Seminar on Statistics and Control of Stochastic Processes. For the past three decades, the seminar has determined the development, in a number of important directions, of the theory of random processes not only in the USSR (now Russia) but in the whole world. It was organised by A N Shiryaev in collaboration with N V Krylov and R Sh Liptser. It started off with optimal stopping and filtering with applications to engineering, and very soon extended its interests to more general problems of stochastic control, causal and anticipating stochastic calculus, limit theorems for semimartingales, martingale methods in queueing theory, foundations of statistics of random processes and, in recent years, mathematical finance. Many studies, for example of stochastic PDEs or extended stochastic integrals, anticipated largely Western works.The contributions in this book are devoted to the hottest topics and united by a martingale methodology which was the key idea of the seminar.