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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 316, Pages 207–221
DOI: https://doi.org/10.4213/tm4244 (Mi tm4244) 		 
Superprocesses for the Population of Rabbits on Grassland

Lina Jia, Jie Xiongb

a Faculty of Computational Mathematics and Cybernetics, Shenzhen MSU–BIT University, Shenzhen, 518172, China
b Department of Mathematics & National Center for Applied Mathematics (Shenzhen), Southern University of Science and Technology, Shenzhen, 518055, China
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DOI: https://doi.org/10.4213/tm4244
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.
Keywords: branching particle system, martingale problem, stochastic partial differential equation, weak uniqueness.
Funding agency Grant number
China Postdoctoral Science Foundation 2020M68194
National Natural Science Foundation of China 61873325
11831010
Southern University of Science and Technology Fund Y01286110
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).
Received: March 29, 2021
Revised: August 28, 2021
Accepted: November 2, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 316, Pages 195–208
DOI: https://doi.org/10.1134/S008154382201014X
Bibliographic databases:
UDC: 519.218.2
MSC: 60J80, 60J85, 60H20
Language: Russian
Citation: Lina Ji, Jie Xiong, “Superprocesses for the Population of Rabbits on Grassland”, Branching Processes and Related Topics, Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin, Trudy Mat. Inst. Steklova, 316, Steklov Math. Inst., Moscow, 2022, 207–221; Proc. Steklov Inst. Math., 316 (2022), 195–208
Citation in format AMSBIB
\Bibitem{JiXio22}
\by Lina~Ji, Jie~Xiong
\paper Superprocesses for the Population of Rabbits on Grassland
\inbook Branching Processes and Related Topics
\bookinfo Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 316
\pages 207--221
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4244}
\crossref{https://doi.org/10.4213/tm4244}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 316
\pages 195--208
\crossref{https://doi.org/10.1134/S008154382201014X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129094503}
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