Conditional log-Laplace functional for a class of branching processes in random environments

A conditional log-Laplace functional(CLLF) for a class of branching processes in random environments is derived. The basic idea is the decomposition of a dependent branching dynamic into a no-interacting branching and an interacting dynamic generated by the random environments.CLLF will play an important role in the investigation of branching processes and superprocesses with interaction.