Socha L. — Linearization Methods for Stochastic Dynamic Systems :: Электронная библиотека попечительского совета мехмата МГУ

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Socha L. — Linearization Methods for Stochastic Dynamic Systems

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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

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Год издания: 2008

Количество страниц: 383

Добавлена в каталог: 14.11.2008

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Предметный указатель

Non - Gaussian excitation      77
Non - Gaussian External Excitation      74
Non - Gaussian process      23
Non - Gaussian Processes      20
Non - Gaussian variable      11
Nonanticipating function      31 32
Nonanticipating functionals      35 36 42
Nonanticipating functions      33
Nondecreasing right continuous function      36
Nondifferentiable      29
Nondifferentiable functions      1
Nonhomogeneous equation      59
Nonlinear      1
Nonlinear function      22
Nonlinear oscillator      1
Nonlinear oscillators      42
Nonlinear scalar function      89
Nonlinear system of algebraic equations      108
Nonlinear time-dependent functions      59 60
Nonlinear vector function      103
Nonlinear vibrating systems      41
Nonnegative definite function      18
Nonnegative definiteness      14
Nonstationary Gaussian External Excitation      65
Norm in Euclidean space      35
Normalized constant      23
Normalized Hermitian polynomials      76
Norms      109
numerical      43
Numerical methods      108
Numerical simulation of realizations      31
Observation time      31
Odd order      22
One-dimensional nonlinearity      104 105
Operation of averaging      7
Operational transfer function      70-72
Operator      38
Operators      38
Or normal process      20
Or normal processes      20
Order of quasi-moments      10
Ordinary Schwartz generalized functions      29
Orthogonal basis      23
Orthogonal expansion      17
Orthogonal sequence in $L^{2}[0, T]$       28
Orthonormal basis      17
Parametric excitation      61 63
Partial derivatives      32
Partial differential equation      26
Physical nonrealizability      30
Piecewise continuous function      17
Piecewise linear-modulated white noise      79
Poisson-driven pulses      80
Polynomial Gaussian Excitation      75
Polynomial of filtered coloured noises      75
Polynomials of coordinates of vector $\textbf{x}$       88
Power spectral density function      19 30 31 39
Power spectral density functions      30
Power spectral density matrix      70 71
Probability density function      7 9 10 26 27
Probability measure      24
Procedure       110
Process with independent increments      27
Processes with continuous parameter      25
Property of homogeneity      24
Quadratic form      34
Quadratic Gaussian Excitation      74
Quasi-moments      10 11 100 122
Random phase modulation      77
Random sequence      12
Random variables      7
Rayleigh      76
Real parts      64
Real stochastic process with continuous time      12
Realization of a real Gaussian process      21
realizations      29
Realizations of process      21
Regular      41
Regular realizations      39
Regularity of solution      41
Response characteristics      2
Response spectrum      79
Riemann integral      16
Riemann's sum      31
Riemann's sums      16
Runge - Kutta method      108
Sample path      12
Scalar Ito stochastic differential equation      89
Scalar product      17 37
Schemes of the solution of stochastic differential equations      43
Schwarz inequality      14
Second - Order Stochastic Processes      13
Second-order moments      13 62 64
Semi invariants      8
Separable      21
SEQUENCE      39
Sequence of correlation functions      15
Sequence of processes      40
Signum function      105

Simple Closure Techniques      94
Simulation of non-Gaussian processes      80
Solution of stochastic differential equation      35
Spectral density domain      4
Spectral method      69
Spectral representation      17
Standard statistical linearization      107
Standard white noise      74
Standard Wiener      103
Standard Wiener process      42 59
Standard Wiener processes      60
State space      2
Stationarity      69
Stationary colored noise      72
Stationary Gaussian stochastic process      68
Stationary independent increments      27
Stationary Markov process      42
Stationary non - Gaussian processes      76
Stationary process      19
Stationary solution of a stochastic differential equation      68
Stationary solutions      110
Statistical linearization      1 103 104 107
Stochastic differential      33 34
Stochastic differential equations      35
Stochastic integral      38
Stochastic integrals      31
Stochastic parametric excitations      79
Stochastic process with discrete time      12
Stochastic stability      4 38
Stratonovich      38
Stratonovich equation      38 39
Stratonovich integral      38
Stratonovich stochastic differential equation      38
Stratonovich stochastic integral      32
Stratonovich vector integral      33
Strong solution      35
Structures under earthquake, sea waves      4
Sufficient conditions for the existence of stationary solution      41
Sufficient conditions for the existence of the solution      41
Symmetrization operation      99
Symmetrizing operation      9 96
Symmetry      14
Taylor expansion      1
Taylor formula      1
The mean-square limit      31
The Method of Neglecting Higher - Order Moments or Cumulants      94
The power spectral density function      72 73
Topological vector space      29
Trace of the matrix      34
Trajectory      12
Transfer function      37
Transformation with memory      74 78
Transformation with Memory of the Brownian and Levy Processes      78
Transition function      24
Transition of probability      26
Transition probability function      24
Transpose and complex-conjugated matrix      71
Transposition      14
Triangular matrices      79
Trigonometric Function Representation      76
Two-dimensional linear filter      73
Unbounded variation      29
uniform      25
Unique strong solution      35-37 41
Unit step      79
Unit step envelope function      77
Unit step-modulated white noise      65
van der Pol oscillator      43
Variance matrix      71
Variance of stationary process      18
Vector      108
Vector continuous non - Gaussian processes      22
Vector diffusion process      33
Vector Ito stochastic differential equation      103
Vector nonlinear function      86
Vector nonlinear Ito stochastic differential equation      86
Vector of mean values      9
Vector standard Wiener process      86
Vector state      65 86 103
Vector stationary Gaussian colored noise      63
Vector stochastic integral      33
Vectors of intensities of noise      103
Voltera second-order integral equations      79
Weakly stationary processes      18
Weighting function      10
White      29
white light      30
White noise      29
Wideband process      31
Wideband processes      39
Wiener process      27
Wind excitation      4
Zero-mean Gaussian process      22
Zero-mean Gaussian processes      22
Zero-mean Gaussian random variables      28
Zero-mean Gaussian white noise      67
Zero-mean second-order processes      40
Zero-mean second-order stochastic processes      30
Zero-mean stationary process      20

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