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Upper and Lower Bounds for Suprema of Chaos Processes
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2018 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Övre och undre gränser för supremum av en kaosprocess (Swedish)
Abstract [en]

There are diverse techniques of analyzing a stochastic process (Xt)t2T . In the following,Talagrand's generic chaining will be introduced and bounds for the expected supremum E[supt2T Xt] of different stochastic processes proved.

The main focus lies on a result of Krahmer, Mendelson and Rauhut who were able to prove an alternative inequality for a specific kind of chaos process. As this bound leads to significantly better results in some applications, the sharpness of this inequality and a possible improvement will be investigated.

Abstract [sv]

Det finns olika tekniker för att analysera en stokastisk process (Xt)t2T . I följande kommer Talagrands generic chaining att införas och gränser för väntevärdet av supremum E[supt2T Xt] av olika stokastiska processer att bevisas.

Huvudfokus ligger på ett resultat av Krahmer, Mendelson och Rauhut som kunde bevisa en alternativ ojämlikhet för en viss typ av kaosprocess. Eftersom den gränsen leder till betydligt bättre resultat i vissa applikationer, kommer skärpan i denna ojämlikhet och en eventuell förbättring att undersökas.

Place, publisher, year, edition, pages
2018.
Series
TRITA-SCI-GRU ; 2018:384
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-236054OAI: oai:DiVA.org:kth-236054DiVA, id: diva2:1260016
External cooperation
TU München
Subject / course
Mathematics
Educational program
Master of Science in Engineering -Engineering Physics
Supervisors
Examiners
Available from: 2018-10-31 Created: 2018-10-31 Last updated: 2018-10-31Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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Language
  • de-DE
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  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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