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	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.

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