LIMITS OF ONE-DIMENSIONAL DIFFUSIONS
成果类型：
Article
署名作者：
Lowther, George
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/08-AOP397
发表日期：
2009
页码：
78-106
关键词：
摘要：
In this paper, we took at the properties of limits of a sequence of real valued inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions, then the limit does not have to be a diffusion. However, we show that as long as the drift terms satisfy a Lipschitz condition and the limit is continuous in probability, then it will lie in a class of processes that we refer to as the almost-continuous diffusions. These processes are strong Markov and satisfy an almost-continuity condition. We also give a simple condition for the limit to be a continuous diffusion. These results contrast with the multidimensional case where, as we show with an example, a sequence of two-dimensional martingale diffusions can converge to a process that is both discontinuous and non-Markov.