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Stationarity and ergodicity for an affine two-factor model. (English) Zbl 1305.60067

Summary: We study the existence of a unique stationary distribution and ergodicity for a two-dimensional affine process. Its first coordinate process is supposed to be a so-called {\(\alpha\)}-root process with \(\alpha \in (1, 2]\). We prove the existence of a unique stationary distribution for the affine process in the case \(\alpha \in (1, 2]\); furthermore, we show ergodicity in the case \(\alpha = 2\).

MSC:

60J25 Continuous-time Markov processes on general state spaces
37A25 Ergodicity, mixing, rates of mixing
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