A stochastic Lotka–Volterra model disturbed by G-Brownian motion (G-LVM for short) in the framework of non-linear expectation is proposed in this paper. This model takes into account the uncertainty of variance of the noise. We prove the G-LVM exists a unique solution and the solution does not tend to infinity when the time is finite under some constraints, and obtain many asymptotic moment estimations which depend on the variance of G-Brownian motion by capacity theory, exponential martingale inequality and analytical skills.

中文翻译：

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G-布朗运动驱动的随机Lotka-Volterra模型的渐近矩估计

本文提出了一种在非线性期望框架下受G-布朗运动（简称G-LVM）干扰的随机Lotka-Volterra模型。该模型考虑了噪声方差的不确定性。我们证明了 G-LVM 存在唯一解，并且在某些约束条件下，当时间有限时，该解不会趋于无穷大，并通过容量理论，指数鞅不等式得到许多依赖于G-布朗运动方差的渐近矩估计和分析能力。