Path transformations of first passage bridges
By Jean Bertoin, L. Chaumont, Jim Pitman. 2003
55 citations recorded by the source corpus.
We define the first passage bridge from 0 to $\lambda$ as the Brownian motion on the time interval $[0,1]$ conditioned to first hit $\lambda$ at time 1. We show that this process may be related to the Brownian bridge, the Bessel bridge or the Brownian excursion via some path transformations, the main one being an extension of Vervaat's transformation. We also propose an extension of these results to certain bridges with cyclically exchangeable increments.
Subfields: Finance, Mathematical Physics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/c20cd07c835310579f974dfb42cffbf134ac9a44
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
In Mathematical Physics
- Jérémie Bettinelli
- Jim Pitman
- Grégory Miermont
- Lancelot F. James
- Jean-François Le Gall
- Alexander V. Gnedin
- Matthias Winkel
- Igor Prünster
In Molecular Biology
- Jérémie Bettinelli
- Jim Pitman
- Lancelot F. James
- Grégory Miermont
- Alexander V. Gnedin
- Igor Prünster
- Antonio Lijoi
- Mark F. J. Steel
Citations in the corpus
- Scaling Limit of Random Planar Quadrangulations with a Boundary (2011, methodology): “Finally, the construction of discrete first-passage bridges from discrete bridges provided in [6], Theorem 1, yields”
- Combinatorial Stochastic Processes (2006, background): “See also [96],[91],[48] for further variations of Vervaat’s transformation.”
- Scaling Limits for Random Quadrangulations of Positive Genus (2010, background): “As p([2])(0) = 12 , we find that p[10g−4](0) = ( 25g−2(5g − 3)! )−1 .”