Lectures on probability and second order random fields

Lectures on probability and second order random fields

by Bricio Hernández, Diego

Type Book
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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 tra…

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Title Statements

  • Full title :Lectures on probability and second order random fields / Diego Bricio Hernández

Summary

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

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

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Edition Statements

  • Publication Date:©1995

Publication Statements

The Physical Object

  • Description:1 Online-Ressource (xii, 146 Seiten) : Illustrationen

Edition Identifiers

  • ISBN:9810219083, 9789810219086, 9789812831613, 9812831614
  • oclc:on1005226007
  • LC Classification:QA274.45
  • Dewey Decimal:519.2

Subjects

Champs aléatoires Probabilités Probabilities PROBABILITY Random fields

Writers

Bricio Hernández, Diego

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