<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-7.xsd"><mods:titleInfo><mods:title>Large deviation based design of an interacting particle method to compute moment generating functions</mods:title></mods:titleInfo><mods:typeOfResource authority="primo">dissertations</mods:typeOfResource><mods:name type="personal"><mods:namePart>Liu, Mengjie</mods:namePart><mods:role><mods:roleTerm type="text">creator</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Dupuis, Paul</mods:namePart><mods:role><mods:roleTerm type="text">Advisor</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Nguyen, Oanh</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart>Harrison, Matthew</mods:namePart><mods:role><mods:roleTerm type="text">Reader</mods:roleTerm></mods:role></mods:name><mods:name type="corporate"><mods:namePart>Brown University. Department of Applied Mathematics</mods:namePart><mods:role><mods:roleTerm type="text">sponsor</mods:roleTerm></mods:role></mods:name><mods:originInfo><mods:copyrightDate>2025</mods:copyrightDate></mods:originInfo><mods:physicalDescription><mods:extent>, None p.</mods:extent><mods:digitalOrigin>born digital</mods:digitalOrigin></mods:physicalDescription><mods:note type="thesis">Thesis (Ph. D.)--Brown University, 2025</mods:note><mods:genre authority="aat">theses</mods:genre><mods:abstract>This thesis introduces a novel interacting particle scheme that combines large deviation analysis with the standard splitting method and rare event analysis to compute the moment generating function for ergodic Markov processes. The proposed scheme differs fundamentally from existing methods, as the thresholds that trigger splitting depend on both space and time.&#13;
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We introduce a quasi-stationary distribution and the Feller property, both of which are essential for analyzing the scheme. We derive the interacting particle schemes based on space and timedependent thresholds, proving the unbiasedness of the estimator. Furthermore, we establish a theorem that bounds the second moment of the proposed unbiased estimator in terms of key parameters of the scheme.&#13;
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The thesis not only establishes new theoretical results but also provides numerical evidence demonstrating the effectiveness of our method.</mods:abstract><mods:subject authority="fast" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/00992659"><mods:topic>Large deviations</mods:topic></mods:subject><mods:language><mods:languageTerm authority="iso639-2b">English</mods:languageTerm></mods:language><mods:recordInfo><mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource><mods:recordCreationDate encoding="iso8601">20250310</mods:recordCreationDate></mods:recordInfo></mods:mods>