标题： Doi-Peliti方法的冗余基解释及其应用 显示英文标题

标题： Redundant basis interpretation of Doi-Peliti method and an application

摘要： Doi-Peliti方法对于研究经典随机过程是有效的，并且有广泛的应用，包括场论方法。 此外，它不仅适用于主方程，也适用于随机微分方程；可以从随机微分方程中推导出一种离散过程。 一个显著的事实是，Doi-Peliti方法与另一种分析方法，即生成函数有关。 与生成函数方法的联系有助于理解从随机微分方程推导离散过程的过程。 在这里，提出了对Doi-Peliti方法的一种冗余基解释，这使我们能够推导出不同类型的离散过程。 传统的生成函数方法对应关系也得到了扩展。 所提出的扩展为我们提供了一种新的工具来研究随机微分方程。 作为所提出解释的应用，我们对从噪声van der Pol系统中推导出的离散过程的有限状态近似进行了数值实验；与具有相同状态数的传统离散过程相比，冗余基给出了合理的结果。 显示英文摘要

摘要： The Doi-Peliti method is effective for investigating classical stochastic processes, and it has wide applications, including field theoretic approaches. Furthermore, it is applicable not only to master equations but also to stochastic differential equations; one can derive a kind of discrete process from stochastic differential equations. A remarkable fact is that the Doi-Peliti method is related to a different analytical approach, i.e., generating function. The connection with the generating function approach helps to understand the derivation of discrete processes from stochastic differential equations. Here, a redundant basis interpretation for the Doi-Peliti method is proposed, which enables us to derive different types of discrete processes. The conventional correspondence with the generating function approach is also extended. The proposed extensions give us a new tool to study stochastic differential equations. As an application of the proposed interpretation, we perform numerical experiments for a finite-state approximation of the derived discrete process from the noisy van der Pol system; the redundant basis yields reasonable results compared with the conventional discrete process with the same number of states.