数学物理学报 ›› 1981, Vol. 1 ›› Issue (2): 195-206.
吴承训, 郭懋正
Wu Chengxun, Guo Maozheng
摘要: In the present paper we study the limit distributions of one-dimensional diffusion processes under non-local boundary conditions. We obtain the existence conditions for the non-trivial stationary distributions, get their concrete formulas in all cases according to boundary classification, and give the results of some probability explanations. One-dimensional diffusion processes, which provide a simple mathematical model for studying irreversible steady systems, show that the basic characteristic of an irreversible stationary state is the occurrence of the probability current, i. e. the circulation phenomenon.