论文标题
Gompertz和Logistic随机动力学：正在进行的任务中的进步
Gompertz and logistic stochastic dynamics: Advances in an ongoing quest
论文作者
论文摘要
在本报告中，我们总结了求解随机微分方程（SDE）的几种方法以及描述Gompertz和Logistic随机动力学的相应Fokker-Planck方程。结果表明，Gompertz SDE的解决方案是完全已知的，而对于Logistic SDE，我们提供了解决方案作为明确的过程，但是我们还不能以封闭形式写下其分布。本文及其附录中列出了许多可能的方法的细节。我们还简要讨论执行合适平均或确定性限制的前景。还建议将这些方程与随机控制领域中的量子谐波振荡器的随机力学联系起来：特别是我们建议研究与量子固定状态相关的方程
In this report we summarize a few methods for solving the stochastic differential equations (SDE) and the corresponding Fokker-Planck equations describing the Gompertz and logistic random dynamics. It is shown that the solutions of the Gompertz SDE are completely known, while for the logistic SDE's we provide the solution as an explicit process, but we can not yet write down its distributions in closed form. Many details of possible ways out of this maze are listed in the paper and its appendices. We also briefly discuss the prospects of performing a suitable averaging, or a deterministic limit. The possibility is also suggested of associating these equations to the stochastic mechanics of a quantum harmonic oscillator adopted as a tool serviceable also in the field of stochastic control: in particular we propose to investigate the equations associated to the quantum stationary states
