Byrnes J.S., Byrnes J.L., Hargreaves K.A., Berry K. (eds.) Probabilistic and Stochastic Methods in Analysis, with Applications

Amsterdam: Springer, 1992. — 687 p.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.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 functionsInnovations 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 architecturesRandom surface geometries with applications to image processingSome 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 ℜ n and maximum entropy
The phase behaviour of ultraflat unimodular polynomials
Fixed points in mixed spectrum analysis
Monte Carlo periodograms
A class of equivalent measuresSecond 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