Curved boundary crossing of bessel processes

Hochschulschrift

Zusammenfassung: We study the first exit time of a Bessel process over a curved boundary and find several asymptotic formulas for the corresponding first exit densities.We start with the examination of the first time at which a multi-dimensional Brownian motion hits a hyperplane and determine its density as well as the joint density of the first hitting time and the location of the first hit. From this we deduce an upper bound for the density of the first exit time of a Bessel process over a straight line.Then, we derive higher-dimensional counterparts of two well-known integral equations for the first exit density of a one-dimensional Brownian motion. They build the basis of our arguments in the following chapters.After that, we obtain two asymptotic representations of the first exit density of a Bessel process over a curved boundary for large times. We only study boundaries that are upperclass functions at infinity and that satisfy certain additional conditions.In the last chapter, we first complete the result of the first chapter by giving a lower bound for the first exit density of a Bessel process over a straight line.This is followed by the examination of first exit densities for distant boundaries. We find that under certain conditions the first exit density over a curved boundary is asymptotically equivalent to the density of the first exit time over the accompanying tangent to this boundary. This result is then further refined.We close the chapter with an example for another possible approach to first boundary crossing problems, the method of images. Our findings in this last section are further confirmation of the preceding results

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Albert-Ludwigs-Universität Freiburg, Dissertation, 2015

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2016
• Creator: Maahs, Ilse
• Contributor: Lerche, Hans Rudolf

Further information

• DOI: 10.6094/UNIFR/10630
• URN: urn:nbn:de:bsz:25-freidok-106307
• Rights: Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 25.03.2025, 1:43 PM CET