On quasi-ergodic distribution for one-dimensional diffusions

Guoman He; Hanjun Zhang

doi:10.1016/j.spl.2015.12.026

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arXiv · 1409.8094

On quasi-ergodic distribution for one-dimensional diffusions

Guoman He·Hanjun Zhang

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Abstract

In this paper, we study quasi-ergodicity for one-dimensional diffusion $X$ killed at 0, when 0 is an exit boundary and $+\infty$ is an entrance boundary. Using the spectral theory tool, we show that if the killed semigroup is intrinsically ultracontractive, then there exists a unique quasi-ergodic distribution for $X$. An example is given to illustrate the result. Moreover, the ultracontractivity of the killed semigroup is also studied.

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Guoman He, Hanjun Zhang. 2014-09-29. On quasi-ergodic distribution for one-dimensional diffusions. https://doi.org/10.1016/j.spl.2015.12.026

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