Probabilistic and Stochastic Methods in Analysis, with Applications

By: J.S. Byrnes (Editor), Kathryn A. Hargreaves (Editor)

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Hardcover | 30 June 1992

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716 Pages

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23.5 x 16.51 x 4.45

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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.

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Wavelets and fractals	p. 2
Wavelets and analysis of partial differential equations	p. 3
Methods of solving dilation equations	p. 15
Characterization of singularities	p. 47
Complex analysis and frames in sampling theory	p. 101
Stationary frames and spectral estimation	p. 117
Density of fuzzy attractors: A step towards the solution of the inverse problem for fractals and other sets	p. 163
Multifractal measures	p. 175
Applications of Gabor and wavelet expansions to the Radon transform	p. 187
Normal numbers and dynamical systems	p. 207
Linear and non-linear decomposition of images using Gabor wavelets	p. 217
Multiresolution analyses, tiles, and scaling functions	p. 233
Applications in engineering	p. 245
Innovations and entropy rate with applications in factorization, spectral estimation, and prediction	p. 247
Generation of accurate broadband information from narrowband data using the Cauchy method	p. 263
Infinite divisibility and the identification of singular waveforms	p. 273
Certain results on spatiotemporal random fields and their applications in environmental research	p. 287
Sharp results on irregular sampling of bandlimited functions	p. 323
Some recent results on the sampling theorem	p. 337
Spectral analysis of random fields with random sampling	p. 343
Application of probabilistic and self-organising neural networks in pattern recognition: a tutorial paper	p. 369
Quantum holography and neurocomputer architectures	p. 383
Random surface geometries with applications to image processing	p. 469
Applications in mathematics and computer science	p. 479
Some continuations of the work of Paley and Zygmund on random trigonometric series	p. 481
Empirical characteristic functional analysis and inference in sequence spaces	p. 517
Is probability a part of mathematical truth?	p. 535
Extension of radial positive-definite distributions in R[superscript n] and maximum entropy	p. 543
The phase behaviour of ultraflat unimodular polynomials	p. 555
Fixed points in mixed spectrum analysis	p. 573
Monte Carlo periodograms	p. 593
A class of equivalent measures	p. 605
Stochastic calculus	p. 615
Second order Hamilton-Jacobi equations in infinite dimensions and stochastic optimal control problems	p. 617
Nuclear space-valued stochastic differential equations with applications	p. 631
A basic view of stochastic integration	p. 649
On the entropy of certain stochastic measures	p. 663
The geometry of attractors for a class of iterated function systems	p. 669
Problems	p. 687
Index	p. 691
Table of Contents provided by Blackwell. All Rights Reserved.

Probabilistic and Stochastic Methods in Analysis, with Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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