| Preface | p. v |
| Dynamical Systems and Their Characteristics | p. 1 |
| Continuous Systems | p. 1 |
| Linear Differential Systems | p. 23 |
| Connections of Systems | p. 42 |
| Stochastic Differential Systems | p. 55 |
| Stochastic Discrete Systems | p. 59 |
| Stochastic Composed Systems. Basic Problems of Stochastic Systems Theory | p. 80 |
| Problems | p. 89 |
| Random Variables, Processes and Functions | p. 97 |
| Probability Spaces | p. 97 |
| Random Variables | p. 102 |
| Conditional Probabilities | p. 110 |
| Probabilities in Finite Product of Spaces | p. 114 |
| Probabilities in Infinite Product of Spaces | p. 125 |
| Existence of Regular Conditional Probabilities | p. 130 |
| Probability Measure of Random Function | p. 133 |
| Separable Random Functions | p. 149 |
| Continuous Random Functions | p. 157 |
| Differentiable Random Functions | p. 167 |
| Problems | p. 176 |
| Moments, Characteristic Functions, Functionals and Canonical Expansions | p. 179 |
| Expectation of Random Function | p. 179 |
| Expectation of Random Variable in Topological Linear Space | p. 187 |
| Moments | p. 190 |
| Conditional Moments | p. 209 |
| Characteristic Functions and Functionals | p. 218 |
| Sequences of Probability Measures and Characteristic Functionals. Distributions in Banach Spaces | p. 230 |
| Normal Distributions in Linear Spaces | p. 246 |
| Approximate Representation of Distributions | p. 266 |
| Canonical Expansions | p. 284 |
| Problems | p. 311 |
| Stochastic Integrals, Spectral and Integral Canonical Representations | p. 319 |
| Mean Square Limits | p. 319 |
| Mean Square Continuity of Random Function | p. 326 |
| Differentiation of Random Functions | p. 330 |
| Integration of Random Function over Nonrandom Measure | p. 336 |
| Integration over Random Measure | p. 343 |
| Stochastic Integral | p. 345 |
| Generalized Random Functions | p. 366 |
| Integral Canonical and Spectral Representations | p. 376 |
| Problems | p. 405 |
| General Theory of Stochastic Systems and Its Applications | p. 425 |
| Stochastic Differentials | p. 425 |
| Stochastic Differential Equations | p. 442 |
| Differential Equations Containing Random Functions | p. 453 |
| Transformation of System Equations into Stochastic Equations | p. 459 |
| Numerical Integration of Stochastic Differential Equation | p. 463 |
| Multi-Dimensional Distributions in Stochastic Differential Systems | p. 479 |
| Multi-Dimensional Distributions in Stochastic Discrete and Continuous-Discrete Systems | p. 506 |
| Distributions in Stochastic Composed Systems | p. 510 |
| Distributions in Stochastic Infinite-Dimensional Systems | p. 518 |
| Applications. Optimal Online Filtering | p. 523 |
| Problems | p. 543 |
| Methods of Linear Stochastic Systems Theory and Their Applications | p. 557 |
| Spectral and Correlation Methods | p. 557 |
| Methods of General Linear Stochastic Systems Theory | p. 575 |
| Methods of Linear Theory of Stochastic Systems based on Canonical Expansions | p. 592 |
| Methods of Linear of Stochastic Systems Theory based on Integral Canonical Representations | p. 613 |
| Applications. Shaping Filters Design and Modeling | p. 624 |
| Applications. Optimal Online Linear Filtering | p. 641 |
| Problems | p. 649 |
| Methods of Nonlinear Stochastic Systems Theory and Their Applications | p. 661 |
| Moments of State Vector | p. 661 |
| Methods of Normal Approximation and Statistical Linearization | p. 673 |
| Methods of General Nonlinear Stochastic Systems Theory. Parametrization of Multi-Dimensional Distributions | p. 691 |
| Methods of Moments and Semiinvariants | p. 695 |
| Methods based on Orthogonal Expansions and Quasimoments | p. 719 |
| Structural Parametrization of Distributions. Ellipsoidal Approximation Method | p. 737 |
| Methods based on Canonical Representations | p. 768 |
| Applications. Analysis of Stochastic Systems and Analytical Modeling | p. 784 |
| Online Conditionally Optimal Nonlinear Filltering | p. 813 |
| Problems | p. 825 |
| Appendices | p. 837 |
| Stochastic Ito Differentials of Typical Composite Functions | p. 837 |
| Hermite Polynomials. Polynomials Orthogonal to Gamma and X[superscript 2]-Distibutions | p. 839 |
| Statistical Linearization of Typical Composite Functions | p. 853 |
| Integrands Evaluation in Equations of Methods based on Parametrization Distributions | p. 856 |
| Basic Characteristics of Some Continuous Typical Linear Systems | p. 864 |
| Structural Transformation Rules | p. 870 |
| Some Definite Integrals and Special Functions | p. 876 |
| Bibliographical Notes | p. 879 |
| References | p. 885 |
| Notations | p. 899 |
| Index | p. 901 |
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