Eigentime identity for one-dimensional diffusion processes. (English) Zbl 1315.60088

Cheng, Li-Juan; Mao, Yong-Hua

J. Appl. Probab. 52, No. 1, 224-237 (2015).

Summary: The eigentime identity for one-dimensional diffusion processes on the halfline with an entrance boundary at \(\infty\) is obtained by using the trace of the deviation kernel. For the case of an exit boundary at \(\infty\), a similar eigentime identity is presented with the aid of the Green function. Explicit equivalent statements are also listed in terms of the strong ergodicity or the uniform decay for diffusion processes.

MSC:

60J60	Diffusion processes
47A75	Eigenvalue problems for linear operators

Keywords:

diffusion processes; eigentime identity; strong ergodicity; hitting time; uniform decay