A SINGULAR 1-D HAMILTON-JACOBI EQUATION, WITH APPLICATION TO LARGE DEVIATION OF DIFFUSIONS | |
Deng, Xiaoxue ; Feng, Jin ; Liu, Yong | |
2011 | |
关键词 | Comparison principle singular Hamiltonian large deviation for singular diffusions |
英文摘要 | The comparison principle (uniqueness) for the Hamilton-Jacobi equation is usually established through arguments involving a distance function. In this article we illustrate the subtle nature of choosing such a distance function, using a special example of one dimensional Hamiltonian with coefficient singularly (non-Lipschitz) depending upon the state variable. The standard method of using Euclidean distance as a test function fails in such situation. Once the comparison is established, we apply it to obtain a new result on small noise Freidlin-Wentzell type probabilistic large deviation theorem for certain singular diffusion processes. This article serves to explain basic ideas behind an abstract approach to comparison developed in [J. Feng and T. G. Kurtz, American Mathematical Society, Providence, Rhode Island. Mathematical Surveys and Monographs, 131, 2006], [J. Feng and M. Katsoulakis, Arch. Ration. Mech. Anal., 192(2), 275-310, 2009] in a simple manner, removing all technicalities due to infinite dimensionality.; Mathematics, Applied; SCI(E); 0; ARTICLE; 1; 289-300; 9 |
语种 | 英语 |
出处 | SCI |
出版者 | communications in mathematical sciences |
内容类型 | 其他 |
源URL | [http://hdl.handle.net/20.500.11897/394825] |
专题 | 数学科学学院 |
推荐引用方式 GB/T 7714 | Deng, Xiaoxue,Feng, Jin,Liu, Yong. A SINGULAR 1-D HAMILTON-JACOBI EQUATION, WITH APPLICATION TO LARGE DEVIATION OF DIFFUSIONS. 2011-01-01. |
个性服务 |
查看访问统计 |
相关权益政策 |
暂无数据 |
收藏/分享 |
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。
修改评论