A theory of martingales for censoring is developed. The Doob-Meyer martingale is shown to be inadequate in general, and a repaired martingale is proposed with a non-predictable centering term. Associated martingale transforms, variation processes, and covariation processes are developed based on a measure of half-predictability that generalizes predictability. The development is applied to study the Kaplan Meier estimator.

翻译：本文发展了一种关于删失的鞅理论。研究表明，Doob-Meyer鞅在一般情况下不适用，因此提出了一种带有不可预测中心项的修正鞅。基于一种推广了可预测性的半可预测性度量，建立了相关的鞅变换、变差过程和协变过程。该理论被应用于研究Kaplan-Meier估计量。