Local Time of a Diffusion in a Stable Lévy Environment
نویسنده
چکیده
We consider a one-dimensional diffusion in a stable Lévy environment. We show that the normalized local time process refocused at the bottom of the standard valley with height log t, (LX(t,mlog t + x)/t, x ∈ R), converges in law to a functional of two independent Lévy processes conditioned to stay positive. To prove this result, we show that the law of the standard valley is close to a two-sided Lévy process conditioned to stay positive. We also obtain the limit law of the supremum of the normalized local time. This result has been obtained by Andreoletti and Diel [1] in the case of a Brownian environment.
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