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⩾0m×Rn, where m,n∈Z⩾0 with m+n>0. Our main theorem extends and unifies some known results for OU-type processes on Rn 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.

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