Spatially dependent birth–death processes can be modelled by kinetic models such as the BBGKY hierarchy. Diffusion in infinite dimensional systems can be modelled with Brownian motion in Hilbert space. In this work Doi field theoretic formalism is utilised to establish dualities between these classes of processes. This enables path integral methods to calculate expectations of duality functions. These are exemplified with models ranging from stochastic cable signalling to jump-diffusion processes.

中文翻译：

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空间生灭过程与希尔伯特空间扩散之间的对偶关系

空间相关的出生-死亡过程可以通过动力学模型（如​​BBGKY层次结构）建模。可以用希尔伯特空间中的布朗运动对无限维系统中的扩散进行建模。在这项工作中，Doi领域理论形式主义被用来在这些过程类别之间建立对偶性。这使路径积分方法能够计算对偶函数的期望。这些模型以从随机电缆信令到跳跃扩散过程的模型为例。