半流选择与马尔可夫选择定理
Semiflow selection and Markov selection theorems
摘要：
时间齐次马尔可夫过程的马尔可夫性的确定性模拟是自治微分方程解的半群性质。当一个微分方程的解是唯一的时，半群性质自然产生，并导致半流。在不唯一的情况下，证明了半流可测选择的一个抽象结果。我们概述了半流选择定理在常微分方程、偏微分方程、微分包含等方面的应用。Krylov的Markov选择定理为了强调这种联系，我们包括一个新版本的马尔可夫选择定理有关最近的论文Flandoli和Romito和Goldys等人。
英文摘要：
The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential equation are unique, and leads to a semiflow. We prove an abstract result on measurable selection of a semiflow for the situations without uniqueness. We outline applications to ODEs, PDEs, differential inclusions, etc. Our proof of the semiflow selection theorem is motivated by N. V. Krylov's Markov selection theorem. To accentuate this connection, we include a new version of the Markov selection theorem related to more recent papers of Flandoli & Romito and Goldys et al.
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