Electronic Communications in Probability

Standardness and nonstandardness of next-jump time filtrations

Stéphane Laurent

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The value of the next-jump time process at each time is the date of its the next jump. We characterize the standardness of the filtration generated by this process in terms of the asymptotic behavior at $n=-\infty$ of the probability that the process jumps at time $n$. In the case when the filtration is not standard we characterize the standardness of its extracted filtrations.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 56, 11 pp.

Accepted: 7 July 2013
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G05: Foundations of stochastic processes
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Standard filtration Cosy filtration

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Laurent, Stéphane. Standardness and nonstandardness of next-jump time filtrations. Electron. Commun. Probab. 18 (2013), paper no. 56, 11 pp. doi:10.1214/ECP.v18-2766. https://projecteuclid.org/euclid.ecp/1465315595

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