论文标题
与觅食竞技场方案的随机猎物前进系统的上限和下限
Upper and lower bounds for the solution of a stochastic prey-predator system with foraging arena scheme
论文作者
论文摘要
我们研究了独特的全局强溶液的一些概率方面的二维系统系统的随机微分方程系统，这些方程描述了由高斯噪声扰动的猎物预言模型。我们首先为任何固定的$ t> 0 $建立，几乎可以确保元件的上限和下限$ x（t）$和$ y（t）$的$ y（t）$：这些显式估计值强调了模型的各种参数之间的相互作用，并同意文献中发现的渐近结果。然后，站在上述边界上，我们得出了$（x（t），y（t））$的联合力矩和分布功能的上和下部估计。我们的分析是基于仔细使用用于随机微分方程的比较定理，并利用驱动方程式的噪声的几个特征。
We investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of stochastic differential equations describing a prey-predator model perturbed by Gaussian noise. We first establish, for any fixed $t> 0$, almost sure upper and lower bounds for the components $X(t)$ and $Y(t)$ of the solution vector: these explicit estimates emphasize the interplay between the various parameters of the model and agree with the asymptotic results found in the literature. Then, standing on the aforementioned bounds, we derive upper and lower estimates for the joint moments and distribution function of $(X(t),Y(t))$. Our analysis is based on a careful use of comparison theorems for stochastic differential equations and exploits several peculiar features of the noise driving the equation.
