Discrete time convolutions and elements of Markov renewal theory

Postgraduate Thesis uoadl:2898647 648 Read counter

Unit:
Κατεύθυνση Στατιστική και Επιχειρησιακή Έρευνα
Library of the School of Science
Deposit date:
2020-03-05
Year:
2020
Author:
Kordalis Leonidas
Supervisors info:
Τρέβεζας Σάμης, Λέκτορας, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών.
Original Title:
Discrete time convolutions and elements of Markov renewal theory
Languages:
English
Translated title:
Discrete time convolutions and elements of Markov renewal theory
Summary:
In this thesis, we present an algebraic approach for discrete time convolutions of real and matrix valued functions. We study their properties using some well known algebraic structures such as the Rings and Groups which help for the development of thesis with concrete applications in Probability theory. Special mention is given for the convolutional inverse which plays a fundamental role in order to obtain unique solutions for renewal and Markov renewal equations.

Ultimately, the theory of convolutions is applied for the extension of usual renewal theory in which we admit the possibility that the interrarival time between two or more successive arrival times could be null. This theoretical frame can be used for application in biological systems, but in reliability theory as well, in which the thermal time is more appropriate to describe the evolution of a system. Furthermore, we use convolutional operators in order to obtain the associated results in the usual theory of Markov renewal chains.
Main subject category:
Science
Keywords:
Algebraic structures, Convolutions, Convolutional inverse, Convolutional exponential function, zero-time events, Renewal theory, Markov renewal theory.
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
29
Number of pages:
100
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