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A Topological–Analytical Method for Proving Averaging Theorems on an Infinite Time Interval in a Degenerate Case
AbstractWe present a topological–analytical method for proving some results of the N. N. Bogolyubov averaging method for the case of an infinite...
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On the Averaging Principle for Semilinear Functional Differential Equations with Infinite Delay in a Banach Space
We establish averaging results for semilinear functional-differential equations with infinite delay in an abstract phase space of axiomatically...
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Averaging
This chapter is an introduction to the method of averaging—a far-reaching and rich mathematical subject that has many important applications. Our...
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First Order Periodic Averaging
We have seen averaging results in the Introduction. We will explain now the theory for O(ε) approximations on a long timescale.
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On the Averaging Principle of Caputo Type Neutral Fractional Stochastic Differential Equations
In this manuscript, we study the averaging principle for a class of neutral fractional stochastic differential equations. Firstly, the existence and...
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Second Order Periodic Averaging
To improve the averaging approximation to second order in ε we can be motivated by the necessity of more precision but, more importantly, also by the...
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Quantifying Outcome Functions of Linear Programs: An Approach Based on Interval-Valued Right-Hand Sides
This paper addresses a linear programming problem with interval right-hand sides, forming a family of linear programs associated with each...
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Optimal Control Over Systems of Functional-Differential Equations With Infinite Delay
We consider the optimal control problem for systems with infinite memory whose models are described by functional-differential equations. We prove...
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Linear Methods: Kernels, Variations, and Averaging
In this chapter, we describe linear methods based on kernels or averaging. Principal component analysis (PCA) is a basic method for dimension...
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Alternating Projection Method for Intersection of Convex Sets, Multi-Agent Consensus Algorithms, and Averaging Inequalities
AbstractThe history of the alternating projection method for finding a common point of several convex sets in Euclidean space goes back to the...
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Averaging for Partial Differential Equations
The qualitative and quantitative theory of weakly nonlinear partial differential equations is still fragmented and it is too early to present a...
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Chernoff Iterations as an Averaging Method for Random Affine Transformations
AbstractFor functions defined on a finite-dimensional vector space, we study compositions of their independent random affine transformations that...
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Averaging Theory for Fractional Differential Equations
The theory of averaging is a classical component of applied mathematics and has been applied to solve some engineering problems, such as in the filed...
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Averaging Principle for Two Time-Scales Stochastic Partial Differential Equations with Reflection
In this work, we consider a system of fast and slow time-scale stochastic partial differential equations with reflection, where the slow component is...
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Application of Banach limits to invariant measures of infinite-dimensional Hamiltonian flows
Applying an invariant measure on phase space, we study the Koopman representation of a group of symplectomorphisms in an infinite-dimensional Hilbert...
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Dynamics and Stability Analysis for Stochastic 3D Lagrangian-Averaged Navier–Stokes Equations with Infinite Delay on Unbounded Domains
This paper is devoted to investigating mean dynamics and stability analysis for stochastic 3D Lagrangian-averaged Navier–Stokes (LANS) equations...
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An Averaging Principle for Stochastic Flows and Convergence of Non-Symmetric Dirichlet Forms
We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using...
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Averaging principle and normal deviations for multi-scale stochastic hyperbolic–parabolic equations
We study the asymptotic behavior of stochastic hyperbolic–parabolic equations with slow–fast time scales. Both the strong and weak convergence in the...
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Averaging Method in the Problem of Optimal control for a Perturbed Parabolic Equation
We consider the problem of optimal control formed by a parabolic nonlinear equation with rapidly oscillating coefficients, an additive control...