从基展开的观点看随机过程的对偶性
Duality in stochastic processes from the viewpoint of basis expansions
摘要：
提出了随机过程对偶关系的一种新的推导方法。目前的焦点是随机微分方程和生灭过程之间的对偶。虽然以前的推导方法是基于时间演化算子的观点，目前的推导是基于基扩展。此外，推导所需的工具仅是部分积分，这是相当简单和易于理解的。基展开的观点使我们能够得到各种对偶随机过程。作为示范，基于泰勒型和埃尔米特多项式的对偶过程的推导。
英文摘要：
A new derivation method of duality relations in stochastic processes is proposed. The current focus is on the duality between stochastic differential equations and birth-death processes. Although previous derivation methods have been based on the viewpoint of time-evolution operators, the current derivation is based on basis expansions. In addition, only the tool needed for the derivation is the integration by parts, which is rather simple and understandable. The viewpoint of basis expansions enables us to obtain various dual stochastic processes. As a demonstration, dual processes based on Taylor-type and Hermite polynomials are derived.
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