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

著者

• Soize, Christian

書誌事項

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

C. Soize

（Series on advances in mathematics for applied sciences, v. 17）

World Scientific, c1994

注記

Includes bibliographical references and index

内容説明・目次

内容説明

This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?

目次

• 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.

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詳細情報

• NII書誌ID(NCID): BA2311157X
• ISBN:
  • 9810217552
• LCCN: 94006348
• 出版国コード: si
• タイトル言語コード: eng
• 出版地: Singapore ; Teaneck, N.J.
• ページ数/冊数: xv, 321 p.
• 大きさ: 23 cm
• 分類:
  • LCC : QC20.7.D5
  • DC20 : 530.1/32
• 件名:
  • LCSH : Fokker-Planck equation -- Numerical solutions
  • LCSH : Stochastic differential equations -- Numerical solutions
  • LCSH : Hamiltonian systems
  • LCSH : Diffusion processes
  • LCSH : Mathematical physics
• 親書誌ID:
  • BA11334635