Renewal Theory


Vorlesung: Dienstags, 10.00 - 12.00, M5
Freitags, 10.00 - 12.00, M5
Dozent: Prof. Dr. Gerold Alsmeyer
Assistenz: tba
KommVV: Eintrag der Vorlesung im kommentierten Vorlesungsverzeichnis
Eintrag der Übungen im kommentierten Vorlesungsverzeichnis
Inhalt: Renewal theory deals with the finer structure of random walks with positive drift, that is, sums of independent, identically distributed random variables with positive mean. In the more classical setup these variables are even nonnegative and then typically interpreted as lifetimes, waiting times or interarrival times. A central object is the so-called renewal measure that provides the mean number of visits of the given random walk to subsets of the real line. It arises in the study of many applied probability models, especially in connection with a certain integral equation, called renewal equation. This course aims at an introduction of the central results of the theory, most notably Blackwell's renewal theorem and the Key Renewal Theorem and their connection with the aforementioned integral equation. We will also present a number of applications from various areas of probability like queuing, risk theory and branching processes.
Leistungsnachweis: tba


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Übungstermin: tba