Uniform convergence of stochastic semigroups

For stochastic C0-semigroups on L1-spaces there is a wealth of results that show strong convergence to an equilibrium as t ? ?, given the semigroup contains partial integral operator. This has plenty applications transport equations and in mathematical biology. However, up now operators do not play prominent role theorems which yield uniform rather than only convergence. In this article we prove that, for irreducible semigroups, actually equivalent being partially uniformly mean ergodic. addition Tauberian theorem, also our convergent if it dual satisfies certain irreducibility condition. Our proof based version lower bound theorem Lasota Yorke, combine with various techniques from Banach lattice theory.