Non-classical error bounds in the central limit theorem [Elektronische Ressource] / von Larisa Yaroslavtseva

Description

Non-classical Error Bounds in the Central Limit TheoremDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)von Dipl. Math. Larisa Yaroslavtseva(akademischer Grad, Vorname, Name)geb. am 25.11.1983 in Miass/Russische F orderationgenehmigt durch die Facult at fur Mathematikder Otto-von-Guericke-Universit at MagdeburgGutachter: Prof. Dr. Ulyanov, Vladimir V.(akademischer Grad, Vorname, Name)Prof. Dr. Christoph, Gerd(akademischer Grad, Vorname, Name)eingereicht am: 25.05.2008Verteidigung am: 17.07.2008PrefaceThe classical central limit theorem states the uniform convergence of the dis-tribution functions of the standardized sums of independent and identicallydistributed square integrable real-valued random variables to the standardnormal distribution function. While rst versions of the central limit theoremare already due to Moivre (1730) and Laplace (1812), a systematic study ofthis topic started at the beginning of the last century with the fundamentalwork of Lyapunov (1900, 1901). Meanwhile, extensions of the central limittheorem are available for a multitude of settings. This includes, e.g., Ba-nach space valued random variables as well as substantial relaxations of theassumptions of independence and identical distributions. Furthermore, ex-plicit error bounds are established and asymptotic expansions are employedto obtain better approximations.

Sujets

• Mathematics

Informations

• Publié par: otto-von-guericke-universitat_magdeburg
• Publié le: 01 janvier 2008
• Nombre de lectures: 29
• Langue: English

Extrait

Non-classical Error Bounds in the Central Limit Theorem

Dissertation

zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.)

von Dipl. Math. Larisa Yaroslavtseva (akademischer Grad, Vorname, Name)

geb.am25.11.1983inMiass/RussischeFo¨rderation

genehmigtdurchdieFacult¨atf¨urMathematik derOtto-von-Guericke-Universita¨tMagdeburg

Gutachter: Prof. Dr. Ulyanov, Vladimir V. (akademischer Grad, Vorname, Name) Prof. Dr. Christoph, Gerd (akademischer Grad, Vorname, Name)

eingereicht am: 25.05.2008

Verteidigung am: 17.07.2008