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• W69794270 abstract "Simulation of rare events can be costly with respect to time and computational resources. For certain processes it may be more efficient to begin at the rare event and simulate a kind of reversal of the process. This approach is particularly well suited to reversible Markov processes, but holds much more generally. This more general result is formulated precisely in the language of stationary point processes, proven, and applied to some examples. An interesting question is whether this technique can be applied to Markov processes which are substochastic, i.e. processes which may die if a graveyard state is ever reached. First, some of the theory of substochastic processes is developed; in particular a slightly surprising result about the rate of convergence of the distribution n at time n of the process conditioned to stay alive to the quasi-stationary distribution, or Yaglom limit, is proved. This result is then verified with some illustrative examples. Next, it is demonstrated with an explicit example that on infinite state spaces the reversal approach to analyzing both the rate of convergence to the Yaglom limit and the likely path of rare events can fail due to transience." @default.
• W69794270 created "2016-06-24" @default.
• W69794270 creator A5049785848 @default.
• W69794270 date "2015-01-01" @default.
• W69794270 modified "2023-09-23" @default.
• W69794270 title "Path Properties of Rare Events" @default.
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• W69794270 doi "https://doi.org/10.20381/ruor-2708" @default.
• W69794270 hasPublicationYear "2015" @default.
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