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- W4386501765 abstract "We consider continuous-state branching processes (CB processes) which become extinct almost surely. First, we tackle the problem of describing the stationary measures on $(0,+infty)$ for such CB processes. We give a representation of the stationary measure in terms of scale functions of related L'{e}vy processes. Then we prove that the stationary measure can be obtained from the vague limit of the potential measure, and, in the critical case, can also be obtained from the vague limit of a normalized transition probability. Next, we prove some limit theorems for the CB process conditioned on extinction in a near future and on extinction at a fixed time. We obtain non-degenerate limit distributions which are of the size-biased type of the stationary measure in the critical case and of the Yaglom's distribution in the subcritical case. Finally we explore some further properties of the limit distributions." @default.
- W4386501765 created "2023-09-08" @default.
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- W4386501765 date "2023-09-03" @default.
- W4386501765 modified "2023-10-16" @default.
- W4386501765 title "Stationary measures and the continuous-state branching process conditioned on extinction" @default.
- W4386501765 doi "https://doi.org/10.48550/arxiv.2309.01300" @default.
- W4386501765 hasPublicationYear "2023" @default.
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