The evolution of the growth of an individual in a random environment can be described through stochastic differential equations of the form dY(t) = β(α − Y(t))dt + σdW(t), where Y(t)= h(X t ), X(t) is the size of the individual at age t, h is a strictly increasing continuously differentiable function, α = h(A), where A is the average asymptotic size, and β represents the rate of approach to maturity. The parameter σ measures the intensity of the effect of random fluctuations on growth and W(t) is the standard Wiener process. We have previously applied this monophasic model, in which there is only one functional form describing the average dynamics of the complete growth curve, and studied the estimation issues. Here, we present the generalization of the above stochastic model to the multiphasic case, in which we consider that the growth coefficient β assumes different values for different phases of the animal’s life. For simplicity, we consider two phases with growth coefficients β1 and β2. Results and methods are illustrated using bovine growth data.
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机译：可以通过形式为dY（t）=β（α-Y（t））dt +σdW（t）的随机微分方程来描述个体在随机环境中的生长演化，其中Y（t）= h （X t），X（t）是在t岁时个体的大小，h是严格增加的连续可微函数，α= h（A），其中A是平均渐近大小，β表示接近率成熟。参数σ衡量随机波动对增长的影响强度，而W（t）是标准的维纳过程。我们以前已经应用了这种单相模型，其中只有一种函数形式描述了完整增长曲线的平均动态，并研究了估计问题。在这里，我们将上述随机模型推广到多相情况，在这种情况下，我们认为生长系数β在动物生命的不同阶段采用不同的值。为简单起见，我们考虑具有增长系数β1和β2的两个阶段。使用牛生长数据说明了结果和方法。
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