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Applied methods of the theory of random functions /
Applied Methods of the Theory of Random Functions.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Oxford :
Pergamon Press,
1966.
|
| Edición: | [1st English ed.]. |
| Colección: | International series of monographs in pure and applied mathematics ;
v. 89. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Applied Methods of the Theory of Random Functions; Copyright Page; Table of Contents; PUBLISHER'S NOTE; CHAPTER I. THE GENERAL PROPERTIES OF RANDOM FUNCTIONS; 1. THE THEORY OF RANDOM FUNCTIONS AS A BRANCH OF THE THEORY OF PROBABILITY; 2. THE BASIC NOTATIONS AND FORMULAE OF THE THEORY OF PROBABILITY; 3. RANDOM FUNCTIONS AND METHODS OF DESCRIBING THEM; 4. TYPICAL PROBLEMS, SOLVED BY MEANS OF THE THEORY OF RANDOM FUNCTIONS; 5. PROPERTIES OF THE CORRELATION FUNCTION; 6. THE DIFFERENTIATION AND INTEGRATION OF RANDOM FUNCTIONS
- 7. THE ACTION OF A LINEAR OPERATOR ON A RANDOM FUNCTION 8. A SYSTEM OF RANDOM FUNCTIONS. THE CROSS-CORRELATION FUNCTION; 9. PROBLEMS ON OVERSHOOTS: THE MEAN NUMBER OF OVERSHOOTS OF A RANDOM FUNCTION ABOVE A GIVEN LEVEL, THE MEAN DURATION OF AN OVERSHOOT; CHAPTER II. THE SPECTRAL THEORY OF STATIONARY RANDOM FUNCTIONS; 10. THE SPECTRAL REPRESENTATION OF STATIONARY RANDOM FUNCTIONS; 11. EXAMPLES OF THE CALCULATION OF THE SPECTRAL DENSITY OF A STATIONARY RANDOM PROCESS
- 12. THE SPECTRAL DENSITY OF A LINEAR COMBINATION OF A STATIONARY RANDOM FUNCTION AND ITS DERIVATIVES. THE STATIONARY SOLUTION OF A LINEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS 13. EXAMPLES OF SPECTRAL DENSITIES AND CORRELATION FUNCTIONS IN MORE COMPLICATED CASES; 14. DETERMINATION OF THE CORRELATION FUNCTION OF THE SOLUTION OF A NON-HOMOGENEOUS DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS WHEN THE RIGHT-HAND SIDE IS NON-STATIONARY; 15. LINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS
- 16. THE PROBABILITY CHARACTERISTICS OF THE SOLUTIONS OF A SYSTEM OF LINEAR EQUATIONS 17. THE DENSITY DISTRIBUTION OF THE SOLUTION OF A LINEAR DIFFERENTIAL EQUATION; CHAPTER III. DETERMINATION OF OPTIMAL DYNAMICAL SYSTEMS; 18. STATEMENT OF THE PROBLEM OF THE DETERMINATION OF OPTIMAL SYSTEMS; 19. THE GENERAL SOLUTION OF THE PROBLEM OF DETERMINING (GIVEN THE INFINITE PAST OF THE PROCESS) THE OPTIMAL DYNAMICAL SYSTEM REPRESENTING THE OPERATIONS OF SMOOTHING (FILTERING), EXTRAPOLATION AND DIFFERENTIATION
- 20. FORMULAE FOR THE DETERMINATION OF THE OPTIMAL TRANSFER FUNCTION OF A DYNAMICAL SYSTEM PERFORMING FILTRATION, EXTRAPOLATION AND DIFFERENTIATION IN THE CASE OF RATIONAL SPECTRAL DENSITIES OF SIGNAL AND NOISE 21. PRACTICAL FORMULAE FOR THE OPTIMAL TRANSFER FUNCTION OF A DYNAMICAL SYSTEM WITH DELAY; 22. OPTIMAL SMOOTHING, EXTRAPOLATION AND DIFFERENTIATION FOR A FINITE OBSERVATION TIME; 23. EXAMPLES OF THE DETERMINATION OF OPTIMAL DYNAMICAL SYSTEMS FOR A FINITE OBSERVATION TIME; CHAPTER IV. EXPERIMENTAL METHODS FOR THE DETERMINATION OF CHARACTERISTICS OF RANDOM FUNCTIONS