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Stochastic equations and ergodicity for two‐type continuous‐state branching processes with immigration in Lévy random environments
Author(s) -
Qin Yuming,
Zheng Xiangqi
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6493
Subject(s) - ergodicity , mathematics , uniqueness , type (biology) , branching (polymer chemistry) , stochastic differential equation , state (computer science) , mathematical analysis , statistical physics , ecology , statistics , materials science , composite material , biology , physics , algorithm
This paper establishes a stochastic differential equation system with both positive and negative jumps and proves the existence and uniqueness of the strong solution and presents an equivalent condition for ergodicity of the solution. The strong solution is called two‐type continuous‐state branching processes with immigration in Lévy random environments. The model can be extended to any finite dimensional case.