具有记忆的随机动力系统概率密度的一个表示公式
A representation formula for the probability density in stochastic dynamical systems with memory
摘要：
Marcus随机时滞微分方程（SDDEs）是科学和工程中经常用来描述具有记忆的随机动力系统的一类模型。由于Marcus SDDE的非马尔可夫性质，不存在无穷小生成元，因此控制密度演化行为的传统Fokker-Planck方程对Marcus SDDE不可用。在本文中，我们确定马库斯SDDE与一些马库斯随机微分方程（SDDE）没有延迟，但受到额外的约束。这为证明解的存在唯一性提供了一种有效的方法，并得到了Marcus SDDE的概率密度表示公式。在公式中，Marcus SDDE的概率密度表示为Marcus无延迟的概率密度。
英文摘要：
Marcus stochastic delay differential equations (SDDEs) are often used to model stochastic dynamical systems with memory in science and engineering. Since no infinitesimal generators exist for Marcus SDDEs due to the non-Markovian property, conventional Fokker-Planck equations, which govern the evolution behavior of density, are not available for Marcus SDDEs. In this paper, we identify the Marcus SDDE with some Marcus stochastic differential equation (SDE) without delays but subject to extra constraints. This provides an efficient way to establish existence and uniqueness for the solution, and obtain a representation formula for probability density of the Marcus SDDE. In the formula, the probability density for Marcus SDDE is expressed in terms of that for Marcus SDE without delay.
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