Random clouds and an application to censoring in survival analysis

B. Gail Ivanoff, Ely Merzbach

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The theory of optional stopping is extended from stopping sets to general adapted random sets called 'clouds' and 'anti-clouds', and a stopping theorem is proven for set-indexed martingales. An application to set-indexed survival analysis is given when the data points are indexed by sets and censored very generally by clouds. This type of censoring corresponds to filtering of survival data on ℝ+. A Nelson-Aalen estimator is defined, and shown to be consistent and asymptotically unbiased.

Original languageEnglish
Pages (from-to)259-279
Number of pages21
JournalStochastic Processes and their Applications
Issue number2
StatePublished - Jun 2004


  • Adapted random set
  • Censoring
  • Cloud
  • Estimator
  • Hazard function
  • Set-indexed martingale
  • Survival analysis


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