Abstract
Motivated by the control of rabbits on grassland, a model of a population with branching dynamics in a random environment is constructed. The system is described as the solution to a conditional martingale problem given the random environment which satisfies a stochastic partial differential equation (SPDE). The weak uniqueness of the solution to the system is established by characterizing its conditional log-Laplace transform through the solution to a related nonlinear SPDE.
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Acknowledgments
We would like to express our sincere gratitude to the editors, two anonymous referees and translator for their very helpful comments on the paper.
Funding
The research of L. Ji was supported in part by the fellowship of China Postdoctoral Science Foundation (grant no. 2020M68194). The research of J. Xiong was supported in part by NSFC (grant nos. 61873325, 11831010) and SUSTech fund (grant no. Y01286110).
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Vol. 316, pp. 207–221 https://doi.org/10.4213/tm4244.
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Ji, L., Xiong, J. Superprocesses for the Population of Rabbits on Grassland. Proc. Steklov Inst. Math. 316, 195–208 (2022). https://doi.org/10.1134/S008154382201014X
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DOI: https://doi.org/10.1134/S008154382201014X