# Aldous criterion for tightness in $D[0,1]$

Does anyone know where I can find some useful information about the Aldous criterion for tightness in the space of all cadlag functions $D[0,1]$?

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Aldous criterion is the criterion using bounded stopping times, right? – Davide Giraudo May 19 '12 at 11:01

There is some stuff in Billingsley "convergence of probability measures" second edition (1999).

JF

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If you have the book, can you give the most relevant elements? – Davide Giraudo Jun 22 '12 at 15:24
By the way, welcome to math.stack.exchange. – Davide Giraudo Jun 22 '12 at 15:31

Billingsley- Convergence of Probability Measures 2nd Ed. pp. 176

Kallenberg- Foundations of Modern Probability 2nd Ed. pp. 314

Aldous- Stopping Times and Tightness (article)

Or in the books of Ethier-Kurtz or Jacod-Shiryaev

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Maybe you can find some information about this criterion on the book by Richard F. Bass, Stochastic Processes-Cambridge University Press (2011).

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You should only answer if you know the book definitely does discuss the criterion in question. If you have checked and it does, please include information about where in the book the relevant information can be found. – Michael Albanese Jan 15 at 12:46