عنوان

Probabilistic and Stochastic Methods in Analysis, with Applications

(Number (ISBN

9789401052399

(Number (ISBN

9789401127912

Number

b408801

Title Proper

Probabilistic and Stochastic Methods in Analysis, with Applications

General Material Designation

[Book]

First Statement of Responsibility

edited by J. S. Byrnes, Jennifer L. Byrnes, Kathryn A. Hargreaves, Karl Berry.

Place of Publication, Distribution, etc.

Dordrecht :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

1992.

Series Title

NATO ASI Series, Series C: Mathematical and Physical Sciences,

Volume Designation

372

ISSN of Series

1389-2185 ;

Text of Note

I Wavelets and fractals -- Wavelets and analysis of partial differential equations -- Methods of solving dilation equations -- Characterization of singularities -- Complex analysis and frames in sampling theory -- Stationary frames and spectral estimation -- Density of fuzzy attractors: A step towards the solution of the inverse problem for fractals and other sets -- Multifractal measures -- Applications of Gabor and wavelet expansions to the Radon transform -- Normal numbers and dynamical systems -- Linear and non-linear decomposition of images using Gabor wavelets -- Multiresolution analyses, tiles, and scaling functions -- II Applications in engineering -- Innovations and entropy rate with applications in factorization, spectral estimation, and prediction -- Generation of accurate broadband information from narrowband data using the Cauchy method -- Infinite divisibility and the identification of singular waveforms -- Certain results on spatiotemporal random fields and their applications in environmental research -- Sharp results on irregular sampling of bandlimited functions -- Some recent results on the sampling theorem -- Spectral analysis of random fields with random sampling -- Application of probabilistic and self-organising neural networks in pattern recognition: a tutorial paper -- Quantum holography and neurocomputer architectures -- Random surface geometries with applications to image processing -- III Applications in mathematics & computer science -- Some continuations of the work of Paley and Zygmund on random trigonometric series -- Empirical characteristic functional analysis and inference in sequence spaces -- Is probability a part of mathematical truth? -- Extension of radial positive-definite distributions in ?n and maximum entropy -- The phase behaviour of ultraflat unimodular polynomials -- Fixed points in mixed spectrum analysis -- Monte Carlo periodograms -- A class of equivalent measures -- IV Stochastic calculus -- Second order Hamilton-Jacobi equations in infinite dimensions and stochastic optimal control problems -- Nuclear space-valued stochastic differential equations with applications -- A basic view of stochastic integration -- On the entropy of certain stochastic measures -- The geometry of attractors for a class of iterated function systems -- Problems.

0

Text of Note

Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here. The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.

International Standard Book Number

9789401052399

Title

Springer eBooks

Parallel Title

Proceedings of the NATO Advanced Study Institute, Il Ciocco, Italy, July 14-27, 1991

Distribution (Probability theory).

Fourier analysis.

Mathematics.

Systems theory.

Byrnes, J. S.

Berry, Karl.

Byrnes, Jennifer L.

Hargreaves, Kathryn A.

SpringerLink (Online service)

Date of Transaction

20190307161100.0

Electronic name

[Book]

Y