A peculiar two point boundary value problem

• 成果类型: Article
• 署名作者: Pang, Huadong; Stroock, Daniel W.
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000818
• 发表日期: 2007
• 页码: 1623-1641
• 关键词: simple pde

摘要

In this paper we consider a one-dimensional diffusion equation on the interval [0, 1] satisfying non-Feller boundary conditions. As a consequence, the initial value Cauchy problem fails to preserve nonnegativity or boundedness. Nonetheless, probability theory plays an interesting role in our analysis and understanding of solutions to this equation.