Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes

Abstract

This work is devoted to the study of conservative affine processes on the canonical state space $D=$R_+^m \times \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, i.e., 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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• Affine Jump-Diffusions: Stochastic Stability and Limit Theorems
• Existence of limiting distribution for affine processes
• Existence of densities for multi-type CBI processes
• Almost sure, L_1- and L_2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigration
• Moments and ergodicity of the jump-diffusion CIR process
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Cited by in corpus (6)

• Long-time behavior for subcritical measure-valued branching processes with immigration
• On a class of stochastic partial differential equations with multiple invariant measures
• On the anisotropic stable JCIR process
• Boundary behavior of multi-type continuous-state branching processes with immigration
• Cutoff thermalization for Ornstein-Uhlenbeck systems with small Lévy noise in the Wasserstein distance
• Regularity of transition densities and ergodicity for affine jump-diffusion processes