Averaging Principle for Stochastic Perturbations of Multifrequency Systems

DOI10.1142/S0219493703000747zbMath1050.60078OpenAlexW1997749856MaRDI QIDQ4474374

Mark I. Freidlin, Alexander D. Wentzell

Publication date: 12 July 2004

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493703000747

zbMATH Keywords

random perturbationsAveraging principlemultifrequency averaging

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Averaging method for ordinary differential equations (34C29) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Related Items (17)

AVERAGING PRINCIPLE FOR QUASI-LINEAR PARABOLIC PDEs AND RELATED DIFFUSION PROCESSES ⋮ Long-time behavior of weakly coupled oscillators ⋮ Some remarks on the Smoluchowski-Kramers approximation ⋮ Random perturbations of a periodically driven nonlinear oscillator: escape from a resonance zone ⋮ Damped-driven KdV and effective equations for long-time behaviour of its solutions ⋮ Khasminskii-Whitham averaging for randomly perturbed KdV equation ⋮ EVOLUTION OF ADIABATIC INVARIANTS IN STOCHASTIC AVERAGING ⋮ Nonequilibrium statistical mechanics of a solid immersed in a continuum ⋮ Diffusion processes on an open book and the averaging principle ⋮ Time-Averaging for Weakly Nonlinear CGL Equations with Arbitrary Potentials ⋮ Stochastic three-dimensional rotating Navier-Stokes equations: averaging, convergence and regularity ⋮ Averaging of stochastic flows: twist maps and escape from resonance ⋮ On distribution of energy and vorticity for solutions of 2D Navier-Stokes equation with small viscosity ⋮ Stochastic homogenization of multicontinuum heterogeneous flows ⋮ Stochastic Homogenization of a Convection-Diffusion Equation ⋮ Nonequilibrium statistical mechanics of Hamiltonian rotators with alternated spins ⋮ Rough homogenisation with fractional dynamics

Cites Work

• ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS
• Elliptic Partial Differential Equations of Second Order
• Random perturbations of Hamiltonian systems
• On stochastic behavior of perturbed Hamiltonian systems

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