Homogenization for¶Stochastic Hamilton-Jacobi Equations

By Fraydoun Rezakhanlou, J. Tarver. 2000

126 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a9779a5e2465b5d86f40fad049a82c1925b3ce3e

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In Computational Theory and Mathematics

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In Statistical and Nonlinear Physics

Citations in the corpus

Stochastic homogenization of Hamilton‐Jacobi‐Bellman equations (2006, background): “Homogenization results for stationary ergodic environments are usually obtained by an application of a version of the ergodic theorem (see, for instance, [3, 10, 16, 17, 19]).”
Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case (2009, methodology): “More precisely in [18, 19], the authors deal with the homogenization of a time– dependent equation, and the result is obtained by passing to the limit in the Lax– Oleinik formulae representing the solutions of the equations with the oscillating variables, when the oscillation parameter goes to 0, th”
Large deviations for random walks in a random environment (2003, background): “Some smoothing out of the subadditive functional is needed for it to be effective; see Rezakhanlou and Tarver [4] for an example.”
Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations (2012, methodology): “This fundamental theorem concerning the qualitative theory of stochastic homogenization of Hamilton-Jacobi equations was proved for convex Hamiltonians by one of the authors [32] (see also Rezakhanlou and Tarver [31]) and, more recently, by two of the authors [4] in the generality discussed here.”
Stochastic Homogenization of Level-Set Convex Hamilton–Jacobi Equations (2012, background): “The homogenization of (1.1) for convex Hamiltonians H was first proved by Souganidis [25] and Rezakhanlous and Tarver [23].”
Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media (2005, methodology): “The first homogenization result in the stationary ergodic setting for fully nonlinear, first-order (Hamilton-Jacobi) PDEs was obtained by one of the authors [20] (see also [19]).”
Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments (2011, methodology): “A new proof of the results of [16, 23, 28, 32], which yields only convergence in probability but does not rely on formulae, has recently been found by Lions and Souganidis [24].”
Singular Perturbations of Nonlinear Degenerate Parabolic PDEs: a General Convergence Result (2003, background): “Other contributions are [10, 28, 1, 38, 36, 2, 23, 24]; see also the references therein.”
Stochastic Homogenization of Nonconvex Hamilton‐Jacobi Equations: A Counterexample (2015, result): “149 (2012), no. 2, 342–361. doi:10.1007/s10955-012-0590-y [21] Rezakhanlou, F.; Tarver, J. E. Homogenization for stochastic Hamilton-Jacobi equations.”
Asymptotic and numerical homogenization (2008, methodology): “The homogenization of fully nonlinear, convex, first-order (Hamilton–Jacobi) equations was considered in Souganidis (1999) and Rezankhanlou and Tarver (2000).”
Correctors for the homogenization of Hamilton‐Jacobi equations in the stationary ergodic setting (2003, background): “Although the existence of an approximate corrector has been established in the almost-periodic setting for general Hamiltonians by Ishii [23], and the effective Hamiltonian has been identified by one of the authors [33] in the stationary ergodic setting and for convex Hamiltonians (see also [31]), n”
Stochastic homogenization of Hamilton-Jacobi equations in stationary ergodic spatio-temporal media (2009, background): “In [24], [26], [22], the same difficulties were overcome via uniform continuity of Lε.”