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October 2020 Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes
Martin Friesen, Peng Jin, Barbara Rüdiger
Ann. Appl. Probab. 30(5): 2165-2195 (October 2020). DOI: 10.1214/19-AAP1554

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.

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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

Information

Received: 1 March 2019; Revised: 1 October 2019; Published: October 2020
First available in Project Euclid: 15 September 2020

MathSciNet: MR4149525
Digital Object Identifier: 10.1214/19-AAP1554

Subjects:
Primary: 37A25, 60H10
Secondary: 60J25

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 5 • October 2020
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