A peculiar two point boundary value problem
arXiv:0710.2396 · doi:10.1214/009117906000000818
Abstract
In this paper we consider a one-dimensional diffusion equation on the interval 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.
Published in at http://dx.doi.org/10.1214/009117906000000818 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)