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Path-valued Processes Associated with Tree-valued Processes

Zenghu LI
Beijing Normal University

A family of continuous-state branching processes is constructed as the solution flow of a jump-type stochastic equation system driven by time-space noises. The family can be regarded as an inhomogeneous increasing path-valued branching Markov process. Two nonlocal branching immigration super processes can be defined from the flow. We identify explicitly the branching mechanisms of those processes. The models give different formulations of the tree-valued Markov processes of Aldous and Pitman (1998) and Abraham and Delmas (2012).