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The Fokker-Planck equation for stochastic dynamical systems and its explicit steady state solutions

Author: Christian Soize
Publisher: Singapore ; Teaneck, N.J. : World Scientific, ©1994.
Series: Series on advances in mathematics for applied sciences, v. 17.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This is an analysis of multi-dimensional nonlinear dissipative Hamiltonian dynamical systems, subjected to parametic and external stochastic excitations by the Fokker-Planck equation method.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Christian Soize
ISBN: 9810217552 9789810217556
OCLC Number: 29913185
Description: xv, 321 pages ; 23 cm.
Contents: Stochastic Canonical Equation of Multidimensional Nonlinear Dissipative Hamiltonian Dynamical Systems; Fundamental Examples of Nonlinear Dynamical Systems and Associated Second Order Equation; Brief Review of Probability and Random Variables; Probabilistic Tools I. Classical Stochastic Processes; Probabilistic Tools II. Mean-Square theory of linear integral transformations and of linear Differential Equations; Probabilistic Tools III. Diffusion Processes and Fokker-Planck Equation; Probabilistic Tools IV. Stochastic Integrals and Stochastic Differential Equations; Stochastic Modelling with Stochastic Differential Equations; FKP Equation for the Dissipative Hamiltonian Dynamical Systems; Stationary Response of Dissipative Dynamical Systems, Existence and Uniqueness, Explicit Solution of an Invariant Measure; Complements for the Normalization Condition, Characteristic Function and Moments of the Invariant Measure; Application II. Multidimensional Linear Oscillators Subjected to External and Parametric Random Excitations; Application III. Multidimensional Nonlinear Oscillators with Inertial Nonlinearity Subjected to External Random Excitations; Application Ill. Multidimensional Nonlinear Oscillators Subjected to External and Parametric Random Excitations; Symplectic Change of Variables in the Multidimensional Unsteady FKP Equation.
Series Title: Series on advances in mathematics for applied sciences, v. 17.
Responsibility: C. Soize.

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