  Recently in Barczy, Li and Pap (2015), the notion of a multi-type
continuous-state branching process (with immigration) having d-types was
introduced as a solution to an d-dimensional vector- valued SDE. Preceding
that, work on affine processes, originally motivated by math- ematical finance,
in Duffie, Filipovic and Schachermayer (2003) also showed the existence of such
processes. See also more recent contributions in this direction due to
Gabrielli and Teichmann (2014) and Caballero, Perez Garmendia and Uribe Bravo
(2015). Older work on multi-type continuous-state branching processes is more
sparse but includes Watanabe (1969) and Ma (2013), where only two types are
considered. In this paper we take a completely different approach and consider
multi-type continuous-state branching process, now allowing for up to a
countable infinity of types, defined instead as a super Markov chain with both
local and non-local branching mechanisms. In the spirit of Englander and
Kyprianou (2004) we explore their extinction properties and pose a number of
open problems.
