Yaglom limit for unimodal Lévy processes. (English) Zbl 07788719
In a nutshell, the authors ‘prove universality of the Yaglom limit of Lipschitz cones among all unimodal Lévy processes sufficiently close to the isotropic \(\alpha\)-stable Lévy process. (...) Yaglom limits describe the large-time limiting behaviour of processes conditioned not to become extinct or absorbed.’ As the authors point out, ‘Over the last years the interest in the existence of Yaglom limits and quasi-stationary distributions was steadily growing. This is due to the fact that the topic is mathematically challenging and in various applications it is natural to ask about the limiting behaviour conditional on non-extinction. However, so far the existence of the Yaglom limit for Lévy processes was studied mainly in the one-dimensional setting or in the finite volume setting.’ The result of this paper generalizes results of K. Bogdan et al. [Electron. J. Probab. 23, Paper No. 11, 19 p. (2018; Zbl 1390.31002)].
Reviewer: Alexander Schnurr (Siegen)
MSC:
| 60G51 | Processes with independent increments; Lévy processes |
| 60G18 | Self-similar stochastic processes |
| 60J35 | Transition functions, generators and resolvents |
| 60J50 | Boundary theory for Markov processes |
Citations:
Zbl 1390.31002References:
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