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We study the long-time behavior of affine processes on positive self-adjoiontHilbert-Schmidt operators which are of pure-jump type, conservative and havefinite second moment. For subcritical processes we prove the existence of aunique limit distribution and construct the corresponding stationary affineprocess. Moreover, we obtain an explicit convergence rate of the underlyingtransition kernels to the limit distribution in the Wasserstein distance oforder $p\in [1, 2]$ and provide explicit formulas for the first two moments ofthe limit distribution. We apply our results to the study ofinfinite-dimensional affine stochastic covariance models in the stationarycovariance regime, where the stationary affine process models the instantaneouscovariance process. In this context we investigate the behavior of the impliedforward volatility smile for large forward dates in a geometric affine forwardcurve model used for the modeling of forward curve dynamics in fixed income orcommodity markets formulated in the Heath-Jarrow-Morton-Musiela framework.

Stationary Covariance Regime for Affine Stochastic Covariance Models in Hilbert Spaces