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Averaging principle for diffusion processes

Stochastics and Stochastic Reports, 1998
Liptser and Stoyanov (Stochastics and Stochastics Reports, 32, (1990), pp. 145 163) study the limiting properties of the solution of the stochastic integral equation as when the drift and generator are regular enough to ensure existence of a unique strong solution for each is strictly stationary, ergodic, and independent of the Wiener process Among ...
S.N. Hashemi, A J. Heunis
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THE AVERAGING PRINCIPLE AND THEOREMS ON LARGE DEVIATIONS

Russian Mathematical Surveys, 1978
ContentsIntroduction § 1. Null approximation and normal deviations § 2. Large deviations from the averaged system § 3. Large deviations. Continuation § 4. Moderate deviations § 5. The behaviour of the system over large time intervals § 6. Examples. Remarks § 7. The averaging principle for stochastic differential equations § 8.
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Average Topological Pressure and a Variational Principle

Journal of Dynamical and Control Systems
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Rahimi, Mehdi, Ghodrati, Asghar
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INVARIANCE PRINCIPLES WITH LOGARITHMIC AVERAGING FOR MARTINGALES

Studia Scientiarum Mathematicarum Hungarica, 2001
For discrete martingales we show that empirical measures related to the central limit theorem when appropriately weighted converge weakly toward a Gaussian measure,for almost all trajectories.Thi result enables u to derive a weighted trong law of the large number for which we pecify both weak and trong rate of convergence.
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Averaging Principle: Continuation

1996
Consider a Hamiltonian dynamical system in the plane R2 $${\mathop X\limits^. _t} = \mathop \nabla \limits^ - H({X_t}),{X_0} = x \in {R^2},\mathop \nabla \limits^ - H(x) = \left( {\frac{{\partial H(x)}}{{\partial {x^2}}}, - \frac{{\partial H(x)}}{{\partial {x^1}}}} \right). $$ (5.1)
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The averaging principle and the diagram technique

Physica A: Statistical Mechanics and its Applications, 1975
Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation.
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Averaging Principle for Stochastic Perturbations of Multifrequency Systems

Stochastics and Dynamics, 2003
We consider the averaging principle for deterministic and stochastic perturbations of multidimensional dynamical systems for which coordinates can be introduced in such a way that the "fast" coordinates change in a torus (for Hamiltonian systems, "action-angle coordinates"). Stochastic perturbations of the white-noise type are considered.
Freidlin, M. I., Wentzell, A. D.
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Learning iteratively a classifier with the Bayesian Model Averaging Principle

Pattern Recognition, 2008
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Rudy Sicard   +2 more
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The averaging principle for stochastic difference equations

Ukrainian Mathematical Journal, 1989
By the ``averaging principle'' one means theorems that establish the convergence of the solutions of equations, depending on a parameter and nonhomogeneous with respect to time (deterministic or stochastic), to the solutions of the equations with averaged (with respect to time or randomness) coefficients, as well as the behavior of the magnitude of ...
Anisimov, V. V., Yurachkovskij, A. P.
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SOME ADMISSIBILITY AND DICHOTOMY QUESTIONS. THE AVERAGING PRINCIPLE

Mathematics of the USSR-Izvestiya, 1976
In this paper some questions in the general theory of stability are studied, with a subsequent application to the problem of averaging on the whole axis.Bibliography: 14 titles.
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