Positive recurrent diusions on the line are treated. We study the asymptotic behavior of the transition density in the long term. The problem is equivalent to the study of Krein's correspondence for bounded strings.
Cite this article
Yuji Kasahara, Asymptotic Behavior of the Transition Density of an Ergodic Linear Diffusion. Publ. Res. Inst. Math. Sci. 48 (2012), no. 3, pp. 565–578DOI 10.2977/PRIMS/81