Abstract
It is possible to introduce the concept of a stopping time in an algebraic way, and define for each stopping time a natural sigma-field. This yields a simple theorem about sample path regularity for processes with a complete separable metric state space.
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References
J. L. Doob,Stochastic Processes, Wiley, New York (1953).
D. Revuz and M. Yor,Continuous Martingales and Brownian Motion, Springer, Berlin (1994).
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Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part II.
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Balkema, A.A. Stopping times and sample path regularity. J Math Sci 83, 352–355 (1997). https://doi.org/10.1007/BF02400918
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DOI: https://doi.org/10.1007/BF02400918