A two-type continuous-state branching process in a varying environment is constructed as the pathwise unique strong solution of a system of stochastic integral equations driven by white noise and Poisson random measures.
Two-type continuous-state branching processes in varying environments
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abstract
A basic class of two-type continuous-state branching processes in varying environments are constructed by solving the backward equation determining the cumulant semigroup. The parameters of the process are allowed to be c\`adl\`ag in time and the difficulty brought about by the bottlenecks are overcome by introducing a suitable moment condition.
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Stochastic equations for two-type continuous-state branching processes in varying environments
A two-type continuous-state branching process in a varying environment is constructed as the pathwise unique strong solution of a system of stochastic integral equations driven by white noise and Poisson random measures.