The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least $\approx 10^4$). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications.

翻译：随机模拟算法（SSA）及相应的蒙特卡洛（MC）方法是研究随机过程最常用的方法之一。这些方法依赖于事件间概率密度函数（PDF）的知识以及所有可能事件之间依赖关系的信息。在许多实际应用中，难以预先指定PDF的解析表达式。在已知PDF形状并利用实验数据的情况下，可采用不同优化方案来评估概率密度函数，进而研究系统的性质。然而，此类方法计算量巨大，通常难以实现。我们证明：当实验可获取的性质直接与所涉及事件的频率相关时，可以用解析解替代优化方案中计算量庞大的蒙特卡洛核心部分。这种替代不仅能够更精确地估计过程性质，还能将模拟时间降低至样本量量级（至少$\approx 10^4$）。所提出的解析方法适用于任意PDF形式。通过精确可解案例以及丙烯酸单体可控自由基聚合（CRP）中支化分数的评估，验证了该方法相较于MC过程的准确性、计算效率及优势。该聚合反应可通过约束随机过程建模，而约束系统相当普遍，因此该方法具有广泛的应用前景。