Ebook: Stochastic Processes in Physics and Engineering

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. O. K. Chesterton. The Scandal of Father 'The Hermit Qad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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Content:
Front Matter....Pages i-xi
Statistical Physics and Optimization: Binary Sequences with Small Autocorrelations....Pages 1-16
A MACSYMA/Expert System for Nonlinear Filtering....Pages 17-61
Generalized Solution of Some Stochastic P.D.E.’s in Turbulent Diffusion....Pages 63-74
Nonstandard Techniques in Stochastic Optimal Control Theory....Pages 75-90
Recursive Estimation of Order and Parameters of a Pilot Plant Turbo Generator....Pages 91-105
Attainability and Reversibility of a Golden Age for the Labour-Surplus Economy: A Stochastic Variational Approach....Pages 107-148
Wavelet Transforms and Edge Detection....Pages 149-157
Lie Algebraic Method in Filtering and Identification....Pages 159-176
White Noise Analysis and the Levy Laplacian....Pages 177-184
An Application of Adaptive Optimal Control....Pages 185-192
The Value of an Option Based on an Average Security Value....Pages 193-203
On Asymptotic Localization by Perturbing Operators for Partial Observation of a Stochastic Evolution Equation....Pages 205-222
Adaptive Games....Pages 223-236
Nonlinear Filtering and Smoothing with High Signal-to-Noise Ratio....Pages 237-251
Fractal and Multifractal Structures in Kinetic Critical Phenomena....Pages 253-278
Generalized Levy Distributions as Limit Laws....Pages 279-304
The Oscillator Representation of the Metaplectic Group Applied to Quantum Electronics and Computerized Tomography....Pages 305-344
Stepping Stone Models in Population Genetics and Population Dynamics....Pages 345-355
Power Spectrum and Fredholm Determinant Related to Intermittent Chaos....Pages 357-379
On the Qualitative Behaviour of Interacting Biological Cell Systems....Pages 381-402
Back Matter....Pages 403-415

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Content:
Front Matter....Pages i-xi
Statistical Physics and Optimization: Binary Sequences with Small Autocorrelations....Pages 1-16
A MACSYMA/Expert System for Nonlinear Filtering....Pages 17-61
Generalized Solution of Some Stochastic P.D.E.’s in Turbulent Diffusion....Pages 63-74
Nonstandard Techniques in Stochastic Optimal Control Theory....Pages 75-90
Recursive Estimation of Order and Parameters of a Pilot Plant Turbo Generator....Pages 91-105
Attainability and Reversibility of a Golden Age for the Labour-Surplus Economy: A Stochastic Variational Approach....Pages 107-148
Wavelet Transforms and Edge Detection....Pages 149-157
Lie Algebraic Method in Filtering and Identification....Pages 159-176
White Noise Analysis and the Levy Laplacian....Pages 177-184
An Application of Adaptive Optimal Control....Pages 185-192
The Value of an Option Based on an Average Security Value....Pages 193-203
On Asymptotic Localization by Perturbing Operators for Partial Observation of a Stochastic Evolution Equation....Pages 205-222
Adaptive Games....Pages 223-236
Nonlinear Filtering and Smoothing with High Signal-to-Noise Ratio....Pages 237-251
Fractal and Multifractal Structures in Kinetic Critical Phenomena....Pages 253-278
Generalized Levy Distributions as Limit Laws....Pages 279-304
The Oscillator Representation of the Metaplectic Group Applied to Quantum Electronics and Computerized Tomography....Pages 305-344
Stepping Stone Models in Population Genetics and Population Dynamics....Pages 345-355
Power Spectrum and Fredholm Determinant Related to Intermittent Chaos....Pages 357-379
On the Qualitative Behaviour of Interacting Biological Cell Systems....Pages 381-402
Back Matter....Pages 403-415
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