Abstract
This work is devoted to the study of conservative affine processes on the canonical state space $D=\mathbb{R}_{+}^{m}\times \mathbb{R}^{n}$, where $m+n>0$. We show that each affine process can be obtained as the pathwise unique strong solution to a stochastic equation driven by Brownian motions and Poisson random measures. Then we study the long-time behavior of affine processes, that is, we show that under first moment condition on the state-dependent and $\log $-moment conditions on the state-independent jump measures, respectively, each subcritical affine process is exponentially ergodic in a suitably chosen Wasserstein distance. Moments of affine processes are studied as well.
Citation
Martin Friesen. Peng Jin. Barbara Rüdiger. "Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes." Ann. Appl. Probab. 30 (5) 2165 - 2195, October 2020. https://doi.org/10.1214/19-AAP1554
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