We know that the exact solutions for most of stochastic age-structured capital systems are difficult to find. The numerical approximation method becomes an important tool to study properties for stochastic age-structured capital models. In the paper, we study the numerical solution for stochastic age-dependent capital system based on explicit-implicit algorithm and discuss the convergence of numerical solution. For the practical significance of capital, we need to consider the positivity of the numerical solution. Therefore, we introduce a penalty factor in the stochastic age-dependent capital system to maintain the positivity, and analyze the convergence of the positive numerical solution. Finally, an example is given to verify our theoretical results.

我们知道，很难找到针对大多数随机年龄结构的资本系统的精确解决方案。数值逼近法成为研究随机年龄结构的资本模型的性质的重要工具。本文研究了基于显式-隐式算法的基于年龄的随机资本系统的数值解，并讨论了数值解的收敛性。对于资本的实际意义，我们需要考虑数值解的正性。因此，我们在随机的与年龄相关的资本系统中引入了惩罚因子，以维持积极性，并分析了正数值解的收敛性。最后，给出一个例子来验证我们的理论结果。