Stochastic averaging with a flattened Hamiltonian: A Markov process on a stratified space (a whiskered sphere)

DOI10.1090/S0002-9947-01-02903-8zbMath0987.60045MaRDI QIDQ2759046

Richard B. Sowers

Publication date: 10 December 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Markov processesstratified spacestochastic averaging

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Functional limit theorems; invariance principles (60F17) Transition functions, generators and resolvents (60J35) Stratified sets (58A35)

Related Items (7)

Pinching and twisting Markov processes ⋮ An averaging principle for diffusions in foliated spaces ⋮ A NOISY SYSTEM WITH A FLATTENED HAMILTONIAN AND MULTIPLE TIME SCALES ⋮ Long time existence for the wave equation with a noise term ⋮ Random perturbations of dynamical systems and diffusion processes with conservation laws ⋮ A Strong Averaging Principle for Lévy Diffusions in Foliated Spaces with Unbounded Leaves ⋮ Stochastic Averaging Near a Homoclinic Orbit with Multiplicative Noise

Cites Work

• Asymptotic analysis of deterministic and stochastic equations with rapidly varying components
• Random perturbations of nonlinear oscillators
• A remark on random perturbations of the nonlinear pendulum
• Limit theorem for a dynamical system in the presence of resonances and homoclinic orbits
• Fiber Brownian motion and the ``hot spots problem
• Pinching and twisting Markov processes
• Fast oscillating random perturbations of dynamical systems with conservation laws
• Random perturbations of Hamiltonian systems
• Probability phenomena due to separatrix crossing
• Asymptotic theory of mixing stochastic ordinary differential equations
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