On transition semigroups of $(A,\Psi )$-superprocesses with immigration

Abstract

We study the global properties of transition semigroups $(p_t^{\nu , \Psi , A})$ of $(A, \Psi )$-superprocesses over compact type spaces with possibly nonzero immigration $\nu$ in various function spaces. In particular, we compare the different rates of convergence of $(p_t^{\nu ,\Psi ,A})$ to equilibrium. Our analysis is based on an explicit formula for the Gateaux derivative of $p_t^{\nu ,\Psi , A} F$.