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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 Stochastic 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 Stochastic Integrals and Stochastic Differential Equations.- 1. Introduction.- 2. Stochastic integrals.- 3. Processes defined by stochastic integrals.- 4. Stochastic differential equations.- 5. White noise and stochastic calculus.- 6. Generalizations of the stochastic 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. Stochastic differential forms.- References.- Solutions to Exercises.

Basic concepts; Random variables; Expectation; Conditional probability and expectation; Characteristic functions; Infinite sequences of Random variables; Markov chains; Introduction to statistics.

"Previous edition stochastic Processes in Information and Dynamical Systems by E. Wong, was published by McGraw-Hill, Inc. in 1971." Incluye bibliografía e índice

Random Signak and Noise Lectures on Ergodic Theqv New York: Chelsea Pub-lishing Co., 1956. A. Papoulis, Probability, Random Variables, and Stochmtic ProcessesNote: A revised edition was published in 1984.) Charles S. Williams, Designing Digita/ Filters

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W. B. Davenport, Jr. and W. L. Root, Random Signak and Noise. New York: McGraw-Hill, 1958. Paul R. Halmos, Lectures on Ergodic Theqv. New York: Chelsea Pub-lishing Co., 1956. A. Papoulis, Probability, Random Variables, and Stochmtic Processes. New York: McGraw-Hill, 1965. (Note: A revised edition was published in 1984.) Charles S. Williams, Designing Digita/ Filters. Englewood Cliffs, NJ: Prentice-Hall, 1986. E. Wong, and B. Hajek, Stochastic Processes in Engineering Systems, New York: Springer-Verlag, 1985.

Random Signak and Noise

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W. B. Davenport, Jr. and W. L. Root, Random Signak and Noise. New
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Designing Digita/ Filters

- Charles S Williams

Charles S. Williams, Designing Digita/ Filters.
Englewood Cliffs, NJ:
Prentice-Hall,
1986.