Monitoring a Poisson process subject to gradual changes in the arrival rates where the arrival rates are unknown

We look at a Poisson process where the arrival rates change from λ1 to λ2. We will assume that the arrival rates both before and after the change are unknown. We also assume that this change does not happen abruptly but gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop early.