A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper.

中文翻译：

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从随机微分方程的角度看双曲线模型

提出了与双曲曲线族相关的随机扩散模型的联合和统一愿景。这种方法背后的动机源于这样一个事实，即所有双曲线曲线都验证了马尔萨斯类型的线性微分方程。凭借这一点，并且通过向所述常微分方程添加乘法噪声，扩散过程可以与平均函数是所述曲线的每条曲线相关联。结果过程中的推论是联合提出的，以及为获得通过应用最大似然法得到的方程组的数值解析所必需的初始解而开发的策略。提出的共同观点对于实施将模型拟合到真实数据的必要程序特别有用。