A fair fraction of textbook statements, if taken literally, applies only when condition (D) or (E) is fulfilled. Condition (D) is fulfilled on the rare occasions that the only influence of the environment is through an h-state- and type-independent death probability, or rate, on top of any h-state- or type-dependent ones. Condition (E) is fulfilled in the rather more common cases that the life history can be decomposed into a number of subsequent stages that connect only through single h-states (so that no information about the past is carried over between stages) and no stage is influenced by both X and E together.
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