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1999

SelectedWorks

Articles 1 - 3 of 3

Full-Text Articles in Mathematics

Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr Dec 1999

Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr

Rudolf Kaehr

Report for the EMBASSI Project

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Path Decompositions Of A Brownian Bridge Related To The Ratio Of Its Maximum And Amplitude, Jim Pitman, Marc Yor Jan 1999

Path Decompositions Of A Brownian Bridge Related To The Ratio Of Its Maximum And Amplitude, Jim Pitman, Marc Yor

Jim Pitman

We give two new proofs of Csaki's formula for the law of the ratio 1-Q of the maximum relative to the amplitude (i.e. the maximum minus minimum) for a standard Brownian bridge. The second of these proofs is based on an absolute continuity relation between the law of the Brownian bridge restricted to the event (Q < v) and the law of a process obtained by a Brownian scaling operation after back-to back joining of two independent three-dimensional Bessel processes, each started at v and run until it first hits 1. Variants of this construction and some properties of the joint law of Q and the amplitude are described.

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Finding And Characterizing Unstable Fixed Points By Controlling System Dynamics, Daniel Kaplan Jan 1999

Finding And Characterizing Unstable Fixed Points By Controlling System Dynamics, Daniel Kaplan

Daniel T. Kaplan

No abstract provided.

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