Stochastic Processes in Engineering Systems
Springer-Verlag New York Inc.
978-1-4612-9545-7 (ISBN)
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. Recursiveestimation.- 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.
Reihe/Serie | Springer Texts in Electrical Engineering |
---|---|
Zusatzinfo | 361 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Technik ► Elektrotechnik / Energietechnik | |
Schlagworte | Information • Systems |
ISBN-10 | 1-4612-9545-9 / 1461295459 |
ISBN-13 | 978-1-4612-9545-7 / 9781461295457 |
Zustand | Neuware |
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