Statistical analysis of Lévy processes with application in finance [Elektronische Ressource] / Achim Gegler

Universitat UlmFakultat fur Mathematik undWirtschaftswissenschaftenStatistical Analysis of Levy Processes withApplication in FinanceDissertationzur Erlangung des Doktorgrades Dr. rer. nat.der Fakultat fur Mathematik und Wirtschaftswissenschaften der Universitat Ulmvorgelegt vonAchim Gegleraus Stuttgart2011Amtierender Dekan: Prof. Dr. Paul Wentges1. Gutachter: Prof. Dr. Ulrich Stadtmuller2. Gutachter: Prof. Dr. Rudiger KieselTag der Promotion: 17. Oktober 2011NotationsN,R are respectively the set of all natural numbers and the real numbers.R isdthe conjunction ofR andf 1 ;1g,N is the conjunction ofN andf1g, X is+the d-fold cartesian product of a set X, it is always assumed that d2N.R is+the set (0;1) andR the set [0;1),N is the setN[f0g.00B( ) is the Borel algebra of a set .1(:) is the indicator function, with a boolean argument. If the argument is true,then the indicator function is equal to 1, if it is false then the indicator functionis equal to 0.a^b := minfa;bg and a_b := maxfa;bg.The convergence in probability of random variables, random vectors or stochas-Ptic processes is denoted by! . The convergence in distribution of randomdvariables or random vectors is denoted by! . Weak convergence of a stochas-Dtic process is denoted by! .Weak convergence of a probability measure is denoted by).The identity matrix is denoted by I.The supremum norm is denoted byjjjj and the Euclidian norm byjj.