发表机构
KTH Royal Institute of Technology; University of Oslo; Igor Sikorsky Kyiv Polytechnic Institute（皇家理工学院; 奥斯陆大学; 伊戈尔·西科尔斯基基辅理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对布朗单驱动的双参数随机系统，提出并证明了由状态及其两个偏导数组成的三元组满足自然马尔可夫性质，并通过示例和Girsanov定理扩展至带漂移情形。
AI 中文摘要
我们研究由布朗单驱动的随机系统，并针对其双参数结构提出一种相适应的马尔可夫性质。对于时空齐次的伊藤单，从点$(t,x)$出发的未来演化不仅由单一值$Y(t,x)$决定，还取决于从$(t,x)$发出的水平边和垂直边上的边界数据。因此，我们证明由三元组$(Y,D_1Y,D_2Y)$构成的扩大状态，相对于由布朗单的两个坐标历史生成的过去σ-代数，满足一种自然的马尔可夫性质。该结果通过示例加以说明，展示了布朗单和简单布朗单系统的强鞅性质。我们还回顾了布朗单的Girsanov定理，并利用它来处理带漂移的单。
英文摘要
We study stochastic systems driven by a Brownian sheet and formulate a Markov property adapted to their two-parameter structure. For time-space homogeneous Itô sheets, the future evolution from a point $(t,x)$ is not determined by the single value $Y(t,x)$ alone, but also by the boundary data along the horizontal and vertical edges issuing from $(t,x)$. We therefore show that the enlarged state consisting of the triple $(Y,D_1Y,D_2Y)$ satisfies a natural Markov property with respect to the past sigma-algebra generated by the two coordinate histories of the Brownian sheet. The result is illustrated by examples showing the strong martingale property for the Brownian sheet and for simple Brownian sheet systems. We also recall a Brownian sheet Girsanov theorem and use it to treat drifted sheets.
Comments18 pages
