Existence of limiting distribution for affine processes

Abstract In this paper, sufficient conditions are given for the existence of limiting distribution of a conservative affine process on the canonical state space R ⩾ 0 m × R n , where m , n ∈ Z ⩾ 0 with m + n > 0 . Our main theorem extends and unifies some known results for OU-type processes on R n and one-dimensional CBI processes (with state space R ⩾ 0 ). To prove our result, we combine analytical and probabilistic techniques; in particular, the stability theory for ODEs plays an important role.