Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor
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The existence of the ergodic attractor is shown in Theorems 1 and 2 in this paper, and the existence of qualitative properties exist behind the convergence of the terms λuλ(x), ≠ u(x,T) in the Hamilton-Jacobi-Bellman equations (HJBs) as λ tends to + 0, T goes to +∞, to the unique number.Abstract:
The problem of the convergence of the terms λuλ(x), ≠ u(x,T) in the Hamilton-Jacobi-Bellman equations (HJBs) as λ tends to +0, T goes to +∞, to the unique number is called the ergodic problem of the HJBs. We show in this paper what kind of qualitative properties exist behind this kind of convergence. The existence of the ergodic attractor is shown in Theorems 1 and 2. Our solutions of HJBs satisfy the equations in the viscosity solutions sense.read more
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On the large time behavior of solutions of Hamilton—Jacobi equations
TL;DR: It is proved, under sharp conditions, that as time goes to infinity, solutions converge to solutions of the corresponding stationary equation.
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Ergodicity, Stabilization, and Singular Perturbations for Bellman-Isaacs Equations
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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
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Viscosity solutions of Hamilton-Jacobi equations
TL;DR: In this article, the authors examined viscosity solutions of Hamilton-Jacobi equations, and proved the existence assertions by expanding on the arguments in the introduction concerning the relationship of the vanishing-viscosity method and the notion of viscoity solutions.
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Functional integration and quantum physics
TL;DR: The basic processes Bound state problems Inequalities Magnetic fields and stochastic integrals Asymptotics Other topics References Index Bibliographic supplement Bibliography as discussed by the authors The Basic Process Bound State problems