Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям Socha L. — Linearization Methods for Stochastic Dynamic Systems Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Linearization Methods for Stochastic Dynamic Systems Автор: Socha L. Аннотация: For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. The aim of this book is to give a systematic introduction to and overview of the relatively simple and popular linearization methods available. The scope is limited to models with continuous external and parametric excitations, yet these cover the majority of known approaches. The book contains an application chapter with emphasis on vibration analysis of stochastic mechanical structures as well as a chapter devoted to the assessment of the accuracy of the theoretical methods presented, both with respect to numerical and to experimental studies. The material derives partly from graduate course notes developed by the author for courses and seminars over the past 20 years. Язык: Рубрика: Математика/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2008 Количество страниц: 383 Добавлена в каталог: 14.11.2008 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель - measurable      24 th column      106 th row      106 15 -dimensional standard Wiener process      64 th central moment      86 th correlation moment      86 th moment      86 th order moment has the form      59 -dimensional diffusion process      26 105 measurable      35 - measurable      31 -field of Borel sets in 24 -fields 35 (LQG)      4 Accuracy of linearization      4 Algebraic matrix Lyapunov equation      68 Algebraic methods      79 Algorithms      110 An interval      28 Approximate probability density function      11 23 Approximate probability density functions      23 Approximate response characteristics of dynamic system      2 Approximation      31 40 Approximation of probability density function      88 Approximation techniques      40 Autocorrelation      13 Autocorrelation function      17 19 Autocovariance functions      13 Automatic control systems      1 Averaging operation      16 Averaging operations      106 Basic criteria      104 Bilinear forms      15 Biorthonormal system      10 Block covariance matrix      20 Bounded function      17 Bounded measurable deterministic functions      61 Boundedness      36 Boxcar and gamma envelope functions      79 Boxcar time-modulating function      79 Brownian      74 78 Brownian motion      27 Central limit theorem      40 Central moments      9 100 Central moments of variable      10 Centralized th coordinate of the vector state      104 Chapman - Kolmogorov equation      24 Characteristic function      9 20 Characteristic function of random variable      7 Characteristic functional      12 Characteristic functions space      2 Closed form      62 Closed-form solutions      79 Closure property      15 Closure technique      75 Colored noise      29 Colored noises      39 Coloured noises      30 Complex closure techniques      94 Complex conjugate      13 14 Complex function      15 Complex-valued processes      13 Components of vectors      36 Conditional distribution      24 Conditional initial conditions      36 Conditional property      27 Constant matrices      61 68 Continuity      21 continuous      18 21 29 Continuous and bounded derivatives      37 Continuous covariance function      22 Continuous derivatives      26 32 34 Continuous function      34 Continuous in mean-square sense      15 Continuous state space      25 Continuous vector random variable      10 Continuous vector stochastic process      35 Control engineers      1 Control of nonlinear stochastic systems      4 Convergence      111 Convergent almost everywhere      28 Convex combination      32 Convex set      32 Correlation      18 Correlation degree      30 Correlation function      13 16 19 71-73 Correlation functions      93 Correlation matrix      71 79 Correlation matrix of the solution      69 Correlation moment      93 Correlation moments      92 Covariance function      13 21 Covariance functions      18 Covariance matrix      9 20 21 Creation of moment differential equations      89 Criteria in probability density functions      4 Criterion 2 - 107 Criterion of linearization      1 Cross correlation function      14 Cross correlation matrix function      14 Cross covariance function      14 Cross covariance matrix function      14 Cumulant Method      97 Cumulant neglect closure      100 Cumulants      7 8 12 89 97 98 100 Cumulants of Stochastic Processes      11 cylinders      41 Derivative      30 Describing function method      1 Determinant      20 Determinant of the matrix      10 Differential equation      68 Differential equation for the pth order moment      60 Differential equation with stochastic coefficients      39 Differential equations      39 62 110 Differential equations for central moments      89 Differential equations for correlation moments      93 Differential equations with stochastic parameters      65 Differential in mean-square sense of      15 Differential of a nonlinear function      33 Differentiation      16 31 Differentiation in mean-square sense      15 Diffusion coefficient      32 Diffusion matrix      25 26 32 33 37 Diffusion process      31-34 37 40 Diffusion processes      25 31 Dirac generalized function      12 30 Direct truncation of the approximation series      11 Distribution space      2 Drift vector      25 26 32 37 Duffing oscillator      43 78 90 Edgeworth series      88 Eigenvalues      64 Electromagnetic waves      30 Elementary event      11 Elementary event 12 Elements      1 108 Energy criteria      4 entropy      2 Equality of the first and second moments of nonlinear and linearized variables      104 Equivalent linearization      1 Euclidean norm      25 Even-order moments      22 Evolutionary      79 Evolutionary power spectral density matrix      79 Exact covariance function      65 Existence of strong solution      41 Explicit      43 Explicit solutions      79 Exponentially decaying harmonic correlation function      79 External excitation      60 Family of growing -fields      29 first      62 64 Fokker - Planck - Kolmogorov equation      4 Fokker - Planck - Kolmogorov equation, FPK.      27 formulas      31 Forward Kolmogorov equation      27 Fourier transform      19 70 73 Fourier transform of correlation matrix      70 Frequency domain      2 Frequency shift      74 Fubini theorem      38 Fundamental matrix      37 61 66 69 Gamma envelope function      79 Gaussian      9 20 Gaussian Colored Noise      63 Gaussian distribution      20 27 Gaussian excitation      1 75 78 Gaussian linearization      107 Gaussian process      21 30 Gaussian processes      20 Gaussian random variable      9 Gaussian stationary white noise      77 Gaussian stochastic process      21 Gaussian white noise      60 61 General Karhunen theorem of representation      17 Generalized derivative of a Wiener process      30 Generalized power spectral density function      17 Generalized stochastic process      29 Generalized Wiener - Chinczyn formula      17 Generating function for cumulants      8 Global Lipschitz conditions      41 Gram - Charlier expansion      11 Gram - Charlier series      22 106 Gramm - Charlier      88 Green function method      69 Green function method for stochastic systems      65 Green function methods      65 Harmonic balance      1 Harmonic excitation      77 Hermite polynomial      10 Hermite polynomials      10 23 122 hessian      106 Higher - Order Moment Criteria      111 Higher-order moments      62 Higher-order moments for continuous processes      13 Homogeneous      25 Homogeneous equation      59 Homogeneous system      69 Hysteresis      1 Hysteresis models      4 Identity matrix      34 37 Implicit Euler      43 Independent standard Wiener processes      61 Independent Wiener processes      35 37 Initial condition      26 35 36 59 61 69 Initial condition 42 Input process      71 Integral form      66 Integral Fourier transform      16 Integral in mean-square sense      16 Integration      15 31 Integration in mean-square sense      16 interval      15 Inverse Fourier transform      70 Inverse transform      17 19 Inverse transformation      60 Iterative procedure      108 Ito      38 Ito differentials      86 Ito equation      38 39 Ito formula      33 Ito integral      38 Ito stochastic differential equation      38 Ito stochastic integral      32 Ito vector integral      33 Ito vector stochastic differential equation      63 Joint characteristic function      7 8 Joint probability density function      20 Joint probability distribution      12 Kolmogorov equations      25 Langevin equation      39 Laplace transform      71 Levy processes      74 78 Lie algebra      79 Limit in mean-square sense      15 Limits      110 Linear filter      63 72 Linear filter equations      69 Linear homogeneous Ito stochastic equation      59 Linear Ito vector stochastic differential equation      60 61 Linear operator transforming      16 linear oscillator      65 72 Linear oscillator with non - Gaussian colored noise excitation      74 Linear stochastic differential equations      36 Linear Stochastic Dynamic Systems      59 Linear systems with parametric excitations      79 Linear systems with quadratic criterion under Gaussian excitation      4 Linear systems with time-dependent coefficients      79 Linear transformations      21 Linearization coefficients      1 2 107 Linearization in frequency domain      1 Linearization methods      1 Linearized form      104 Lipschitz condition      36 Lipschitz conditions      41 42 Local Lipschitz conditions      43 Logarithm of characteristic      8 Lyapunov differential equation      110 Lyapunov equation      110 Lyapunov function      42 Lyapunov function approach      41 Maclaurin series      8 Markov process      24 37 Markov processes      23 Martingale with respect to -field { }      27 Mathematical background      1 Mathematical models      1 20 Mathematical tools      3 Matrix correlation function      14 66 67 Matrix covariance function      14 66 Matrix intensity function      67 Matrix variance function      68 Mean      21 Mean value      18 20 21 66 69 Mean-square criterion      110 Mean-square error of approximation      105 Mean-square integral      32 Measurable      36 Measurable and bounded functions      37 Measurable space of functions      35 Memory transformation of Gaussian processes      74 Memoryless transformation of Gaussian processes      74 Method of Central Moments      96 Moment criteria      2 4 Moment differential equations      64 Moment equations      59 86 Moment Equations for Nonlinear Stochastic Dynamic Systems      85 Moments      7 11 12 97 98 Multiindices      89 Mutually independent processes      29 Narrow band non - Gaussian stationary processes      78 Necessary and sufficient condition      15 Necessary conditions for the minimum      106 Negative definite matrix      64 New state variables      75 77 Non - Gaussian Closure Techniques      96 Non - Gaussian Distributions      9
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