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