AI 中文总结
研究可分巴拿赫空间上柱形鞅值测度的鞅表示定理，借助非随机化随机积分新理论等工具，证明了相关定理及推论，还应用结果刻画了由柱形白噪声测度驱动的随机微分方程弱鞅问题的解。
AI 中文摘要
我们证明了在可分巴拿赫空间上定义的柱形鞅值测度的鞅表示定理。建立该定理的主要工具是自反巴拿赫空间中非随机化随机积分的新理论，以及对柱形白噪声测度过程的研究与刻画。作为表示定理的结果，我们证明了希尔伯特空间值测度和柱形平方可积鞅的类似版本。最后，我们应用这些结果来刻画由柱形白噪声测度驱动的随机微分方程弱鞅问题的解。
英文摘要
We prove a martingale representation theorem for cylindrical martingale-valued measures defined on a separable Banach space. The main tool for establishing the theorem, is a new theory of non-radonifying stochastic integration in reflexive Banach spaces. A second one is the study and characterization of cylindrical white noise measure processes. As consequences of our representation theorem, we prove analogous versions for Hilbert space-valued measures and for cylindrical square integrable martingales. Finally, we apply the results to characterize the solutions to the weak martingale problem for SDEs driven by cylindrical white noise measures.
