Homogenization of a class of one-dimensional nonconvex viscous Hamilton-Jacobi equations with random potential
Homogenization of a class of one-dimensional nonconvex viscous Hamilton-Jacobi equations with random potential
复制标题
一类具有随机势的一维非凸粘性 Hamilton-Jacobi 方程的齐次化
DOI：
10.1080/03605302.2019.1657448
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发表时间：
2017
影响因子：
1.9
通讯作者：
O. Zeitouni
中科院分区：
文献类型：
--
作者：
Elena Kosygina;A. Yilmaz;O. Zeitouni
摘要 我们证明了一类具有梯度变量非凸随机哈密顿量的一维粘性 Hamilton-Jacobi 方程的齐次性。由于哈密顿量的特殊形式，这些具有线性初始条件的偏微分方程的解具有涉及随机势中受控布朗运动的指数期望的表示。有效哈密顿量是随着时间趋向无穷大这些指数期望的渐进增长率，并且以随机势中（不受控制的）布朗运动的倾斜自由能的形式明确表示。证明涉及大偏差、构建导致指数鞅的校正器以及渐近最优策略的识别。
Abstract We prove the homogenization of a class of one-dimensional viscous Hamilton-Jacobi equations with random Hamiltonians that are nonconvex in the gradient variable. Due to the special form of the Hamiltonians, the solutions of these PDEs with linear initial conditions have representations involving exponential expectations of controlled Brownian motion in a random potential. The effective Hamiltonian is the asymptotic rate of growth of these exponential expectations as time goes to infinity and is explicit in terms of the tilted free energy of (uncontrolled) Brownian motion in a random potential. The proof involves large deviations, construction of correctors which lead to exponential martingales, and identification of asymptotically optimal policies.
某些类别的非凸有效哈密顿量的最小–最大公式和其他属性
影响因子：
1.4
作者：
Qian, Jianliang;Tran, Hung V.;Yu, Yifeng
通讯作者：
Yu, Yifeng