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Peer-reviewedCC BY 4.0Axioms

Mutually Competing Superprocesses in Independent Random Environments

  • Lina Ji1
  • Huili Liu2
  1. 1MSU-BIT-SMBU Joint Research Center of Applied Mathematics, Shenzhen MSU-BIT University, Shenzhen 518172, China
  2. 2School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
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Abstract

We study the martingale problem for two mutually competing superprocesses in independent Brownian random environments. The competition rates depend on the spatial position and both population measures. Under suitable assumptions, we establish well-posedness for every pair of finite initial measures and derive moment estimates for the total masses. Existence is proved by constructing branching particle systems and establishing the tightness of their empirical measure processes. Uniqueness in law follows from pathwise uniqueness for the system of stochastic partial differential equations satisfied by the associated distribution-function-valued processes.

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Cite

BibTeXRIS
BibTeX
@article{ji2026mutually,
  title = {{Mutually Competing Superprocesses in Independent Random Environments}},
  author = {Lina Ji and Huili Liu},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15110790},
  url = {https://www.mdpi.com/2075-1680/15/11/790},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Mutually Competing Superprocesses in Independent Random Environments
AU  - Lina Ji
AU  - Huili Liu
PY  - 2026
DA  - 2026/10/22
JO  - Axioms
DO  - 10.3390/axioms15110790
UR  - https://www.mdpi.com/2075-1680/15/11/790
AB  - We study the martingale problem for two mutually competing superprocesses in independent Brownian random environments. The competition rates depend on the spatial position and both population measures. Under suitable assumptions, we establish well-posedness for every pair of finite initial measures and derive moment estimates for the total masses. Existence is proved by constructing branching particle systems and establishing the tightness of their empirical measure processes. Uniqueness in law follows from pathwise uniqueness for the system of stochastic partial differential equations satisfied by the associated distribution-function-valued processes.
SN  - 2075-1680
ER  -