Wasserstein-Type Distances of Two-Type Continuous-State Branching Processes in Lévy Random Environments

Shukai Chen (), Rongjuan Fang () and Xiangqi Zheng ()
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Shukai Chen: Fujian Normal University
Rongjuan Fang: Fujian Normal University
Xiangqi Zheng: East China University of Science and Technology

Journal of Theoretical Probability, 2023, vol. 36, issue 3, 1572-1590

Abstract: Abstract Under natural conditions, we prove exponential ergodicity in the $$ L_1$$ L 1 -Wasserstein distance of two-type continuous-state branching processes in Lévy random environments with immigration. Furthermore, we express precisely the parameters of the exponent. The coupling method and the conditioned branching property play an important role in the approach. Using the tool of superprocesses, ergodicity in total variation distance is also proved.

Keywords: Exponential ergodicity; Wasserstein distance; Branching process; Random environment; Superprocess; 60J25; 60J68; 60J80; 60J76 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01211-y

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