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Stochastic Processes in Engineering Systems

Paperback (2nd ed. 1985. Softcover reprint of the original 2nd ed. 1985)
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Product Details

  • ISBN-13: 9781461295457
  • Publisher: Springer New York
  • Publication date: 7/31/2012
  • Series: Springer Texts in Electrical Engineering Series
  • Edition description: 2nd ed. 1985. Softcover reprint of the original 2nd ed. 1985
  • Edition number: 2
  • Pages: 361
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.78 (d)

Table of Contents

1 Elements of Probability Theory.- 1. Events and probability.- 2. Measures on finite-dimensional spaces.- 3. Measurable functions and random variables.- 4. Sequences of events and random variables.- 5. Expectation of random variables.- 6. Convergence concepts.- 7. Independence and conditional expectation.- 2 Shastic Processes.- 1. Definition and preliminary considerations.- 2. Separability and measurability.- 3. Gaussian processes and Brownian motion.- 4. Continuity.- 5. Markov processes.- 6. Stationarity and ergodicity.- 3 Second-Order Processes.- 1. Introduction.- 2. Second-order continuity.- 3. Linear operations and second-order calculus.- 4. Orthogonal expansions.- 5. Wide-sense stationary processes.- 6. Spectral representation.- 7. Lowpass and bandpass processes.- 8. White noise and white-noise integrals.- 9. Linear prediction and filtering.- 4 Shastic Integrals and Shastic Differential Equations.- 1. Introduction.- 2. Shastic integrals.- 3. Processes defined by shastic integrals.- 4. Shastic differential equations.- 5. White noise and shastic calculus.- 6. Generalizations of the shastic integral.- 7. Diffusion equations.- 5 One-Dimensional Diffusions.- 1. Introduction.- 2. The Markov semigroup.- 3. Strong Markov processes.- 4. Characteristic operators.- 5. Diffusion processes.- 6 Martingale Calculus.- 1. Martingales.- 2. Sample-path integrals.- 3. Predictable processes.- 4. Isometric integrals.- 5. Semimartingale integrals.- 6. Quadratic variation and the change of variable formula.- 7. Semimartingale exponentials and applications.- 7 Detection and Filtering.- 1. Introduction.- 2. Likelihood ratio representation.- 3. Filter representation—change of measure derivation.- 4. Filter representation—innovations derivation.- 5. Recursive estimation.- 8 Random Fields.- 1. Introduction.- 2. Homogenous random fields.- 3. Spherical harmonics and isotropic random fields.- 4. Markovian random fields.- 5. Multiparameter martingales.- 6. Shastic differential forms.- References.- Solutions to Exercises.
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