Lectures on probability and second order random fields
This book of lecture notes contains theoretical background material required for computer generation of random fields, which is of interest in various fields of applied mathematics. The necessary probabilistic background suitable for applied work in engineering as well as signal and image processing is also covered. The book is a valuable guide for higher level engineering students.
Read More ↓Title Statements
- Full title :Lectures on probability and second order random fields / Diego Bricio Hernández.
Summary
This book of lecture notes contains theoretical background material required for computer generation of random fields, which is of interest in various fields of applied mathematics. The necessary probabilistic background suitable for applied work in engineering as well as signal and image processing is also covered. The book is a valuable guide for higher level engineering students.
Read More ↓Edition Statements
- Publication Date:©1995.
Publication Statements
- Publisher(s):World Scientific
- Place of Publication:Singapore
- Language:eng
- Publication Date:©1995.
The Physical Object
- Description:1 online resource (xii, 146 pages) : : illustrations
Edition Identifiers
- ISBN:9789812831613, 9812831614
- oclc:ocn842919956
- LC Classification:QA274.45
- Dewey Decimal:519.2
Table of Contents
1. Random variables. 1.1. The concept of probability. 1.2. Random variables. 1.3. Distributions. 1.4. Expected value -- 2. Random vectors. 2.1. Joint distributions. 2.2. Independence. 2.3. Transformations of random vectors -- 3. Sampling random variables. 3.1. Designing a sampling technique. 3.2. Monte Carlo methods. 3.3. Error bounds -- 4. Second order properties. 4.1. Orthogonality. 4.2. Orthogonal projections. 4.3. Conditional expectation. 4.4. Optimal linear estimation -- 5. The Fourier transform. 5.1. Characteristic functions. 5.2. The Fourier transform. 5.3. The Plancherel theorem -- 6. Second order random fields. 6.1. Covariance functions. 6.2. Construction of random fields. 6.3. Analytical properties of random fields. 6.4. Spectral representation of covariances -- 7. Spectral representation of random fields. 7.1. Random measures. 7.2. Stochastic integrals. 7.3. The spectral representation -- 8. Sampling and modeling random fields. 8.1. Sampling orthogonal random measures. 8.2. Fast Fourier computations. 8.3. Simulation and orthogonal expansions. 8.4. Mean and covariance estimation.
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