Abstract Linear fractional Galton–Watson branching processes in i.i.d. random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals. On the other hand, any random difference...

In this note, we prove a new martingale transformation for superprocesses with general branching mechanisms which could be regarded as a Girsanov type transformation in measure-valued setting. As an application, a criterion for global extinction of superprocesses with spatially dependent...