标题： 随机正性保持辛分裂方法对随机Lotka-Volterra捕食-食饵模型的应用 显示英文标题

标题： Stochastic positivity-preserving symplectic splitting methods for stochastic Lotka--Volterra predator-prey model

摘要： 本文提出了求解随机Lotka-Volterra捕食者-猎物模型的两种随机保正辛方法，该模型受乘性噪声驱动。 为了继承原始系统的内在特性，引入了随机Lie-Trotter分裂法和随机Strang分裂法，证明了这两种方法均能保持数值解的正性和具有离散随机辛守恒律。 通过推导数值解的 $p$- 阶矩的一致有界性，我们证明了这两种方法在 $L^2(\Omega)$- 范数下的强收敛阶均为一。 最后，通过二维和四维数值例子验证了理论结果。 显示英文摘要

摘要： In this paper, we present two stochastic positive-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model driven by a multiplicative noise. To inherit the intrinsic characteristic of the original system, the stochastic Lie--Trotter splitting method and the stochastic Strang splitting method are introduced, which are proved to preserve the positivity of the numerical solution and possess the discrete stochastic symplectic conservation law as well. By deriving the uniform boundedness of the $p$-th moment of the numerical solution, we prove that the strong convergence orders of these two methods are both one in the $L^2(\Omega)$-norm. Finally, we validate the theoretical results through two and four dimensional numerical examples.