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Random Perturbations of Hamiltonian Systems
 
Random Perturbations of Hamiltonian Systems
eBook ISBN:  978-1-4704-0100-9
Product Code:  MEMO/109/523.E
List Price: $39.00
MAA Member Price: $35.10
AMS Member Price: $23.40
Random Perturbations of Hamiltonian Systems
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Random Perturbations of Hamiltonian Systems
eBook ISBN:  978-1-4704-0100-9
Product Code:  MEMO/109/523.E
List Price: $39.00
MAA Member Price: $35.10
AMS Member Price: $23.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1091994; 82 pp
    MSC: Primary 60; 35; 34;

    Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.

    Readership

    Specialists in dynamical systems, partial differential equations, probability theory and control theory.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Main results
    • 3. Proof of Theorem 2.2
    • 4. Proofs of Lemmas 3.2, 3.3, 3.4
    • 5. Proof of Lemma 3.5
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1091994; 82 pp
MSC: Primary 60; 35; 34;

Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.

Readership

Specialists in dynamical systems, partial differential equations, probability theory and control theory.

  • Chapters
  • 1. Introduction
  • 2. Main results
  • 3. Proof of Theorem 2.2
  • 4. Proofs of Lemmas 3.2, 3.3, 3.4
  • 5. Proof of Lemma 3.5
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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