Path Properties of Rare Events
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...
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ndltd-uottawa.ca-oai-ruor.uottawa.ca-10393-319482018-01-05T19:02:11Z Path Properties of Rare Events Collingwood, Jesse McDonald, David Rare Events Point Processes Markov Chains Substochastic Yaglom limit Convergence 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 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. 2015-01-20T16:53:26Z 2015-01-20T16:53:26Z 2015 2015 Thesis http://hdl.handle.net/10393/31948 http://dx.doi.org/10.20381/ruor-2708 en Université d'Ottawa / University of Ottawa |
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en |
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Rare Events Point Processes Markov Chains Substochastic Yaglom limit Convergence |
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Rare Events Point Processes Markov Chains Substochastic Yaglom limit Convergence Collingwood, Jesse Path Properties of Rare Events |
description |
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 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. |
author2 |
McDonald, David |
author_facet |
McDonald, David Collingwood, Jesse |
author |
Collingwood, Jesse |
author_sort |
Collingwood, Jesse |
title |
Path Properties of Rare Events |
title_short |
Path Properties of Rare Events |
title_full |
Path Properties of Rare Events |
title_fullStr |
Path Properties of Rare Events |
title_full_unstemmed |
Path Properties of Rare Events |
title_sort |
path properties of rare events |
publisher |
Université d'Ottawa / University of Ottawa |
publishDate |
2015 |
url |
http://hdl.handle.net/10393/31948 http://dx.doi.org/10.20381/ruor-2708 |
work_keys_str_mv |
AT collingwoodjesse pathpropertiesofrareevents |
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1718598211250159616 |