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Random Walks on Random Lattices and ...

White, Ryan Tyle.

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Random Walks on Random Lattices and Their Applications.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Random Walks on Random Lattices and Their Applications./
作者:	White, Ryan Tyle.
面頁冊數:	214 p.
附註:	Source: Dissertation Abstracts International, Volume: 76-10(E), Section: B.
Contained By:	Dissertation Abstracts International76-10B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3663192
ISBN:	9781321854831

Random Walks on Random Lattices and Their Applications.
White, Ryan Tyle.

Random Walks on Random Lattices and Their Applications. - 214 p.

Source: Dissertation Abstracts International, Volume: 76-10(E), Section: B.

Thesis (Ph.D.)--Florida Institute of Technology, 2015.

This item must not be sold to any third party vendors.

This work studies a class of continuous-time, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary are studied extensively by stochastic analysis and operational calculus. Further, information on the process can be ascertained only upon observations occurring according to a delayed renewal process, rather than in real time. Passage times are thus obscured and results are first derived pertaining to the pre-passage and post-passage observations.

ISBN: 9781321854831Subjects--Topical Terms:

515831
Mathematics.

Random Walks on Random Lattices and Their Applications.
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245 1 0 $a Random Walks on Random Lattices and Their Applications.
300 $a 214 p.
500 $a Source: Dissertation Abstracts International, Volume: 76-10(E), Section: B.
500 $a Adviser: J. H. Dshalalow.
502 $a Thesis (Ph.D.)--Florida Institute of Technology, 2015.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a This work studies a class of continuous-time, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary are studied extensively by stochastic analysis and operational calculus. Further, information on the process can be ascertained only upon observations occurring according to a delayed renewal process, rather than in real time. Passage times are thus obscured and results are first derived pertaining to the pre-passage and post-passage observations.
520 $a Two distinct strategies are developed to combat the crudeness of delayed observations in order to derive more refined information about the processes. The first strategy is to introduce intermediate thresholds on some of the coordinates and considers fluctuations about these intermediate boundaries, which can use information observed over time to continually refine the results. The second "time-sensitive" strategy restricts time to a random time interval, e.g. between the pre-passage and post-passage observations, and revives the real-time paths of the process from the delayed time series. This strategy leads to time-dependent probabilistic results, including joint distributions and conditional distributions and probabilities.
520 $a In all models, probabilistic results (joint probability transforms under operators, marginal transforms, moments, distributions, probabilities) associated with passage times, excess levels, and the likelihood of threshold(s) to be crossed are derived, and shown to be analytically and numerically tractable under a variety of special cases. Results are tested for accuracy via stochastic simulation.
520 $a The processes are applied to the detection and prediction of losses to vital networks due to hostile attacks and/or benign failures. The accumulation of losses to a network during a series of loss events is modeled by a 2-dimensional process. The first dimension counts the random numbers of nodes (e.g. routers or operational sites) incapacitated by successive attacks. The nodes have random weights associated with their incapacitation (e.g. loss of operational capacity or cost of repair). The second dimension measures the cumulative weight associated with the nodes lost. The exit from a rectangle corresponds to either type of loss surpassing a threshold, and represents the network entering a critical state.
590 $a School code: 0473.
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical mathematics. $3 3173530
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710 2 $a Florida Institute of Technology. $3 718970
773 0 $t Dissertation Abstracts International $g 76-10B(E).
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791 $a Ph.D.
792 $a 2015
793 $a English
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