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Book
Optimal stopping rules
Authors: ---
ISBN: 1281116319 9786611116316 3540740112 3540740104 Year: 2008 Publisher: Berlin ; New York : Springer,

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Abstract

Although three decades have passed since first publication of this book reprinted now as a result of popular demand, the content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The "ground floor" of Optimal Stopping Theory was constructed by A.Wald in his sequential analysis in connection with the testing of statistical hypotheses by non-traditional (sequential) methods. It was later discovered that these methods have, in idea, a close connection to the general theory of stochastic optimization for random processes. The area of application of the Optimal Stopping Theory is very broad. It is sufficient at this point to emphasise that its methods are well tailored to the study of American (-type) options (in mathematics of finance and financial engineering), where a buyer has the freedom to exercise an option at any stopping time. In this book, the general theory of the construction of optimal stopping policies is developed for the case of Markov processes in discrete and continuous time. One chapter is devoted specially to the applications that address problems of the testing of statistical hypotheses, and quickest detection of the time of change of the probability characteristics of the observable processes. The author, A.N.Shiryaev, is one of the leading experts of the field and gives an authoritative treatment of a subject that, 30 years after original publication of this book, is proving increasingly important.


Book
Controlled diffusion processes
Authors: ---
ISBN: 0387904611 3540904611 9783540904618 9780387904610 Year: 1980 Volume: 14 Publisher: New York (N.Y.): Springer,


Book
Optimal stopping rules
Authors: ---
Year: 1978 Publisher: New York, Heidelberg, Berlin Springer

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Book
Gaussian random processes
Authors: --- ---
ISBN: 038790302X 354090302X 1461262771 1461262755 9780387903026 Year: 1978 Volume: 9 Publisher: New York (N.Y.): Springer,

Statistics of random processes.. 1, General theory
Authors: --- ---
ISBN: 3540639292 3540639284 364208365X 3662100282 3642083668 3662130432 9783540639299 Year: 2001 Volume: 5-6 Publisher: Berlin: Springer,

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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.


Book
Controlled diffusion processes
Authors: --- ---
Year: 1980 Volume: 14 Publisher: New York : Springer-Verlag,

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Book
Statistics of Random process : general theory and applications
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Year: 1977 Publisher: New York, Heidelberg, Berlin Springer

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Book
Gaussian random processes
Authors: --- ---
Year: 1970 Publisher: New York, Heidelberg, Berlin Springer

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