Solutions of a class of stochastic Poisson systems

doi:10.7523/j.ucas.2020.0057

Journal of University of Chinese Academy of Sciences ›› 2022, Vol. 39 ›› Issue (6): 721-726.DOI: 10.7523/j.ucas.2020.0057

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Solutions of a class of stochastic Poisson systems

WANG Yuchao, WANG Lijin

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2020-07-16 Revised:2020-10-09 Online:2022-11-15
Contact: WANG Lijin, E-mail: ljwang@ucas.ac.cn
Supported by:
National Natural Science Foundation of China (11971458, 11471310， and 11071251)

Abstract

Abstract: In this paper, a class of stochastic Poisson systems, arising from randomly perturbing a type of Lotka-Volterra systems by certain Stratonovich white noise, are considered. We give the sufficient conditions for the almost sure existence (global non-explosion) and uniqueness of the solution of the system, and further prove that the solution is positive and bounded almost surely under the proposed conditions. Numeraical experiments are performed to verify the results.

Key words: stochastic Poisson systems, Lotka-Volterra systems, Stratonovich SDEs, invariants, non-explosion

CLC Number:

O241. 8

WANG Yuchao, WANG Lijin. Solutions of a class of stochastic Poisson systems[J]. Journal of University of Chinese Academy of Sciences, 2022, 39(6): 721-726.

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Solutions of a class of stochastic Poisson systems

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