论文标题
随机Lotka-Volterra竞争性反应扩散系统受时空白噪声扰动：建模和分析
Stochastic Lotka-Volterra Competitive Reaction-Diffusion Systems Perturbed by Space-Time White Noise: Modeling and Analysis
论文作者
论文摘要
本文由传统的Lotka-Volterra竞争模型激励，提出并分析了一类随机反应 - 扩散部分微分方程。与文献中的模型相反，新的配方可以使该物种的空间依赖性。此外，噪声过程被允许是时空白噪声。在这项工作中，考虑了良好的性，解决方案的规律性，密度的存在以及存在非液体和非线性生长系数和非线性生长系数和乘法噪声的随机反应扩散系统的不变度度量。通过在SPDE中使用随机场方法和无限整合理论方法进行轻度溶液，进行了分析。然后，本文在一般环境下开发了Lotka-Volterra竞争系统。在随机演算中的新开发的工具的帮助下，研究了长期属性。
Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation enables spatial dependence of the species. In addition, the noise process is allowed to be space-time white noise. In this work, wellposedness, regularity of solutions, existence of density, and existence of an invariant measure for stochastic reaction-diffusion systems with non-Lipschitz and non-linear growth coefficients and multiplicative noise are considered. By combining the random field approach and infinite integration theory approach in SPDEs for mild solutions, analysis is carried out. Then this paper develops a Lotka-Volterra competitive system under general setting; longtime properties are studied with the help of newly developed tools in stochastic calculus.
