Path Properties of Rare Events

FieldValue
dc.contributor.authorCollingwood, Jesse
dc.date.accessioned2015-01-20T16:53:26Z
dc.date.available2015-01-20T16:53:26Z
dc.date.created2015
dc.date.issued2015
dc.identifier.urihttp://hdl.handle.net/10393/31948
dc.identifier.urihttp://dx.doi.org/10.20381/ruor-2708
dc.description.abstractSimulation 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 pi(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.
dc.language.isoen
dc.publisherUniversité d'Ottawa / University of Ottawa
dc.subjectRare Events
dc.subjectPoint Processes
dc.subjectMarkov Chains
dc.subjectSubstochastic
dc.subjectYaglom limit
dc.subjectConvergence
dc.titlePath Properties of Rare Events
dc.typeThesis
dc.faculty.departmentMathématiques et statistique / Mathematics and statistics
dc.contributor.supervisorMcDonald, David
dc.degree.namePhD
dc.degree.leveldoctorate
dc.degree.disciplineSciences / Science
thesis.degree.namePhD
thesis.degree.levelDoctoral
thesis.degree.disciplineSciences / Science
uottawa.departmentMathématiques et statistique / Mathematics and statistics
CollectionThèses, 2011 - // Theses, 2011 -

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