Unit:
Κατεύθυνση Στατιστική και Επιχειρησιακή ΈρευναLibrary of the School of Science
Author:
Oikonomidis Iakovos-David
Supervisors info:
Χελιώτης Δημήτριος, Αναπληρωτής Καθηγητής, Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών.
Βαγγελάτου Ευτυχία, Επίκουρη Καθηγήτρια, Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών.
Μπούτσικας Μιχαήλ, Αναπληρωτής Καθηγητής, Στατιστικής Και Aσφαλιστικής Eπιστήμης, Πανεπιστήμιο Πειραιώς.
Original Title:
Μελέτη χρόνων διακοπής μέσω της ταυτότητας του Wald και εφαρμογές.
Translated title:
Α study of stopping times using Wald's identity and applications
Summary:
The main aim of this work is the overview (theoretical presentation and
methods for determining the distribution of a stopping time or a
stop sum through a general form of Wald identity that
is based on an appropriate change of probability measure. Initially, there will be a presentation of basic concepts of probabilities and stochastic process
which are necessary for the formulation of the main results, such as e.g.
martingales, stopping times, change of probability measure etc. In its main part
specific applications of stopping times and stop sums in various research areas such as e.g. in ruin theory
(time until ruin occurs), theory of reliability (time to failure of a system), runs and scans statistics theory
(time until the appearance of specific pattern) and more generally exit times of a stochastic process from an appropriate set.
Main subject category:
Science
Keywords:
Wald's identity, Stopping times, Martingales, Random walk, Run and scan statistics, Change of probability measure, Esscher transform, Generating functions, Ruin theory
