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Strong feller and ergodic properties of the (1+1)-affine process

Part of: Stochastic analysis Markov processes

Published online by Cambridge University Press:  14 March 2023

Shukai Chen  and
Zenghu Li
Shukai Chen*
Affiliation:
Fujian Normal University
Zenghu Li*
Affiliation:
Beijing Normal University
*
*Postal address: School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350007, People’s Republic of China. Email address: skchen@mail.bnu.edu.cn
**Postal address: Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People’s Republic of China. Email address: lizh@bnu.edu.cn
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Abstract

We prove some estimates for the variations of transition probabilities of the (1+1)-affine process. From these estimates we deduce the strong Feller and the ergodic properties of the total variation distance of the process. The key strategy is the pathwise construction and analysis of several Markov couplings using strong solutions of stochastic equations.

Keywords

Affine processstrong Feller propertyergodicitytotal variation distancecoupling

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes 60H15: Stochastic partial differential equations
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 3 , September 2023 , pp. 812 - 834
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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