Itô-Wentzell 公式与 Kunita 公式的几何推广
A Geometric Extension of the Itô-Wentzell and Kunita's Formulas
AI总结：
本文将 Itô-Wentzell 公式推广到流形上的张量值随机过程，推导随机微分同胚流下拉回与前推的 KIW 公式，以服务随机流体动力学和噪声适定性研究。
摘要：
我们将描述由连续半鞅驱动的时变随机场沿连续半鞅演化的 Itô-Wentzell 公式，推广到流形上取值于张量场的随机过程。更具体地，我们研究由连续半鞅驱动的时变随机张量场，在随机微分同胚流作用下的拉回（相应地，前推）如何随时间演化，并在适当的正则性条件下将其推导出来。我们称该结果为关于张量值随机过程平流的 Kunita-Itô-Wentzell（KIW）公式。此类方程在随机流体动力学和噪声导致适定性问题中具有重要意义，有助于推动现有理论中某些几何推广的发展。
英文摘要：
We extend the Itô-Wentzell formula for the evolution along a continuous semimartingale of a time-dependent stochastic field driven by a continuous semimartingale to tensor field-valued stochastic processes on manifolds. More concretely, we investigate how the pull-back (respectively, the push-forward) by a stochastic flow of diffeomorphisms of a time-dependent stochastic tensor field driven by a continuous semimartingale evolves with time, deriving it under suitable regularity conditions. We call this result the Kunita-Itô-Wentzell (KIW) formula for the advection of tensor-valued stochastic processes. Equations of this nature bear significance in stochastic fluid dynamics and well-posedness by noise problems, facilitating the development of certain geometric extensions within existing theories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
