A conditioned continuous-state branching process with applications

Rongjuan Fang and Zenghu Li

Statistics & Probability Letters, 2019, vol. 152, issue C, 43-49

Abstract: A supercritical CB-process conditioned on explosion is again a Markov process. We characterize the transition semigroup of the conditioned process by its Laplace transform and by a Doob’s h-transform. The conditioned CB-process is constructed as the strong solution of a stochastic integral equation. We use the distribution of the conditioned process to construct directly the canonical Kuznetsov measure of the CB-process. The later is reconstructed from positive paths picked up by a Poisson random measure based on the canonical Kuznetsov measure.

Keywords: Conditioned CB-process; Doob’s h-transform; Entrance rule; Stochastic integral equation; Canonical Kuznetsov measure (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2019.04.013

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