Ebook: Statistics of Random Processes: II. Applications

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.

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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.

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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.
Content:
Front Matter....Pages I-XV
Conditionally Gaussian Processes....Pages 1-16
Optimal Nonlinear Filtering: Interpolation and Extrapolation of Components of Conditionally Gaussian Processes....Pages 17-53
Conditionally Gaussian Sequences: Filtering and Related Problems....Pages 55-97
Application of Filtering Equations to Problems of Statistics of Random Sequences....Pages 99-143
Linear Estimation of Random Processes....Pages 145-175
Application of Optimal Nonlinear Filtering Equations to some Problems in Control Theory and Estimation Theory....Pages 177-218
Parameter Estimation and Testing of Statistical Hypotheses for Diffusion-Type Processes....Pages 219-259
Random Point Processes: Stieltjes Stochastic Integrals....Pages 261-308
The Structure of Local Martingales, Absolute Continuity of Measures for Point Processes, and Filtering....Pages 309-353
Asymptotically Optimal Filtering....Pages 355-382
Back Matter....Pages 383-402

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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.
Content:
Front Matter....Pages I-XV
Conditionally Gaussian Processes....Pages 1-16
Optimal Nonlinear Filtering: Interpolation and Extrapolation of Components of Conditionally Gaussian Processes....Pages 17-53
Conditionally Gaussian Sequences: Filtering and Related Problems....Pages 55-97
Application of Filtering Equations to Problems of Statistics of Random Sequences....Pages 99-143
Linear Estimation of Random Processes....Pages 145-175
Application of Optimal Nonlinear Filtering Equations to some Problems in Control Theory and Estimation Theory....Pages 177-218
Parameter Estimation and Testing of Statistical Hypotheses for Diffusion-Type Processes....Pages 219-259
Random Point Processes: Stieltjes Stochastic Integrals....Pages 261-308
The Structure of Local Martingales, Absolute Continuity of Measures for Point Processes, and Filtering....Pages 309-353
Asymptotically Optimal Filtering....Pages 355-382
Back Matter....Pages 383-402
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