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On Averaging Principles: An Asymptotic Expansion Approach
SIAM Journal on Mathematical Analysis, 2004Asymptotic properties of a diffusion process having fast and slow components are examined. The work is devoted to the formulation of an optimal stochastic control problem as a singularly perturbed system providing an alternative for treating complex systems. Asymptotic properties of the solutions to the Kolmogorov backward equations are studied.
Rafail Z. Khasminskii, Gang George Yin
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Variational Principles and Weighted Averages
Journal of Mathematical Physics, 1967An examination of two functionals, which are in common use for making variational estimates of weighted averages, reveals that one may be preferred over the other in certain cases. In particular, for a positive-definite self-adjoint operator, the normalization-independent functional always yields the better approximation to the stationary value.
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Large Deviation Principle of Nonconventional Ergodic Averages
Journal of Statistical Physics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jung-Chao Ban, Wen-Guei Hu, Guan-Yu Lai
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Moderate Deviations and Invariance Principles for Sample Average Approximations
SIAM Journal on Optimization, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gao, M, Yiu, KFC
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Mixed stochastic differential equations: Averaging principle result
Applied Mathematics Letters, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Min Han, Yong Xu 0011, Bin Pei
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Utilitarianism: the Classical Principle and the Average Principle
Canadian Journal of Philosophy, 1975Act Utilitarianism has traditionally been regarded as the view that you should always perform the action that will bring about the greatest possible excess of happiness over unhappiness or, if there is no such alternative, the least possible excess of unhappiness over happiness.1Following Rawls, I shall call this the classical principle. An alternative
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The Averaging Principle. Fluctuations in Dynamical Systems with Averaging
1984Let us consider the system $$\begin{array}{*{20}{c}} {\dot Z_t^\varepsilon = \varepsilon b(Z_t^\varepsilon ,{\xi _t}),}&{Z_0^\varepsilon = x} \end{array}$$ (1.1) of ordinary differential equations in R r , where ξt, t ≥ 0, is a function assuming values in R r e is a small numerical parameter and $$b(x,y) = ({b^1}(x,y), \ldots ,{b^r}(x,y)).
Mark I. Freidlin, Alexander D. Wentzell
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The Average-Value Correspondence Principle
AIP Conference Proceedings, 2007In previous work [1], we have presented an attempt to derive the finite‐dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we continue the derivation of the quantum formalism by formulating a correspondence principle, the Average‐Value Correspondence Principle, that allows relations between ...
Philip Goyal +5 more
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Averaging Principles for the Swift-Hohenberg Equation
Communications on Pure and Applied Analysis, 2020 This work studies the effects of rapid oscillations (with respect to time) of the forcing term on the long-time behaviour of the solutions of the Swift-Hohenberg equation. More precisely, we establish three kinds of averaging principles for the Swift-Hohenberg equation, they are averaging principle in a time-periodic problem, averaging principle on a ...
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Invariance principles for logarithmic averages
Mathematical Proceedings of the Cambridge Philosophical Society, 1992AbstractWe obtain weak and strong Gaussian approximations for logarithmic averages of indicators of normalized partial sums. The proofs are based on invariance principles for integrals of an Ornstein–Uhlenbeck process and on strong approximations of normalized partial sums by Orstein–Uhlenbeck processes.
Csörgő, Miklós, Horváth, Lajos
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