Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes

Friesen, Martin; Jin, Peng; Rüdiger, Barbara

doi:10.1214/19-aap1554

Cited by 22 publications

(53 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Based on methods of stochastic calculus, similar results were obtained for affine processes with state-space in [5, Lemma 3.4] and on the canonical state space in [19, Lemma 5.2]. For affine processes on , i.e., continuous-state branching processes with immigration, and also for the more general class of Dawson–Watanabe superprocesses, an alternative approach based on a fine analysis of the Laplace transform is provided in [39].…”

Section: Resultsmentioning

confidence: 61%

“…Note that, by an argument similar to (15), one easily finds that for all . Exponential ergodicity in different Wasserstein distances for affine processes on the canonical state space was very recently studied in [19]. Below we provide a corresponding result for affine processes on .…”

Section: Resultsmentioning

confidence: 79%

“…The proof of Theorem 2.5, which is given in Section 8, largely follows some ideas of [19]. In contrast to the latter work, for the study of affine processes on we encounter similar difficulties as in the proof of Theorem 2.3.…”

Section: Resultsmentioning

confidence: 99%

“…Based on strong solutions to the stochastic equation and the construction of monotone couplings, an alternative approach for the study of the long-time behavior of affine processes on the canonical state space was recently given in [19]. This approach certainly does not apply here since it is still an open problem whether each affine process on can be obtained as a strong solution to a certain stochastic equation driven by Brownian motions and Poisson random measures (it is actually not even known what such a stochastic equation in the general case should look like).…”

Section: Resultsmentioning

confidence: 99%

“…Finally, let us mention that the long-time behavior of affine processes has previously been studied in many different settings, either based on a detailed study of the characteristic function (see e.g. [46], [39], [20], [47], [34], [32], [36], [30]), by stochastic stability criteria due to Meyn and Tweedie ([4], [29], [44]), or by coupling techniques ([19], [18], [40]). One application of such study is towards the estimation of parameters for affine models.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

et al. 2020

Self Cite

View full text Add to dashboard Cite

This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite $d\times d$ matrices. In particular, for conservative and subcritical affine processes we show that a finite $\log$ -moment of the state-independent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: first, in a specific metric induced by the Laplace transform, and second, in the Wasserstein distance under a first moment assumption imposed on the state-independent jump measure and an additional condition on the diffusion parameter.

show abstract

Section: Resultsmentioning

confidence: 61%

Section: Resultsmentioning

confidence: 79%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

Regularity of transition densities and ergodicity for affine jump‐diffusions

Friesen

Jin

Kremer

et al. 2022

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

This paper studies the transition density and exponential ergodicity for affine processes on the canonical state space ℝ 𝑚 ≥0 × ℝ 𝑛 . Under a Hörmander-type condition for diffusion components as well as a boundary nonattainment condition, we derive the existence and regularity of the transition densities and then prove the strong Feller property of the associated semigroup. Moreover, we also show that, under an additional subcriticality condition on the drift, the corresponding affine process is exponentially ergodic in the total variation distance.

show abstract

Coupling methods and exponential ergodicity for two‐factor affine processes

Bao

Wang

2023

Mathematische Nachrichten

View full text Add to dashboard Cite

In this paper, by invoking the coupling approach, we establish exponential ergodicity under the 𝐿 1 -Wasserstein distance for two-factor affine processes. The method employed herein is universal in a certain sense so that it is applicable to general two-factor affine processes, which allow that the first component solves a general Cox-Ingersoll-Ross (CIR) process, and that there are interactions in the second component, as well as that the Brownian noises are correlated; and even to some models beyond two-factor processes.

show abstract

Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes

Cited by 22 publications

References 57 publications

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

Regularity of transition densities and ergodicity for affine jump‐diffusions

Coupling methods and exponential ergodicity for two‐factor affine processes

Contact Info

Product

Resources

About