Ben Povar (Univ. of Warwick)
We study the joint convergence of Bienaymé-Galton-Watson processes with immigration (BGWI) and its ``naive'' local times at 0 to the corresponding Continuous Branching Process with immigration (CBI) and its local time at 0. We do this by analysing the structure of excursions from zero and around positive levels and looking at the convergence of the hitting times of the BGWI to the hitting times of CBI. The research is done jointly with Aleksandar Mijatovic and Gerónimo Uribe Bravo.
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