Bibliographic Details
| Title: |
The greatest convex minorant of Brownian motion, meander, and bridge. |
| Authors: |
Pitman, Jim1 pitman@stat.berkeley.edu, Ross, Nathan1 ross@stat.berkeley.edu |
| Superior Title: |
Probability Theory & Related Fields. Aug2012, Vol. 153 Issue 3/4, p771-807. 37p. 2 Graphs. |
| Subject Terms: |
*WIENER processes, *MATHEMATICAL decomposition, *POINT processes, *MARKOV processes, *MATHEMATICAL models, *MATHEMATICAL analysis, *APPLIED mathematics |
| Abstract: |
This article contains both a point process and a sequential description of the greatest convex minorant of Brownian motion on a finite interval. We use these descriptions to provide new analysis of various features of the convex minorant such as the set of times where the Brownian motion meets its minorant. The equivalence of these descriptions is non-trivial, which leads to many interesting identities between quantities derived from our analysis. The sequential description can be viewed as a Markov chain for which we derive some fundamental properties. [ABSTRACT FROM AUTHOR] |
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| Database: |
Academic Search Premier |