Journal article
Derivative martingale of the branching Brownian motion in dimension d ≥ 1
- Abstract:
- We consider a branching Brownian motion in R d . We prove that there exists a random subset Θ of S d−1 such that the limit of the derivative martingale exists simultaneously for all directions θ ∈ Θ almost surely. This allows us to define a random measure on S d−1 whose density is given by the derivative martingale. The proof is based on first moment arguments: we approximate the martingale of interest by a series of processes, which do not take into account particles that travelled too far away. We show that these new processes are uniformly integrable martingales whose limits can be made to converge to the limit of the original martingale.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
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(Preview, Accepted manuscript, 529.7KB, Terms of use)
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- Publisher copy:
- 10.1214/20-AIHP1131
Authors
- Publisher:
- Institute of Mathematical Statistics
- Journal:
- Annales de l'Institut Henri Poincaré, Probabilités et Statistiques More from this journal
- Volume:
- 57
- Issue:
- 3
- Pages:
- 1786-1810
- Publication date:
- 2021-07-22
- Acceptance date:
- 2020-11-17
- DOI:
- ISSN:
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0246-0203
- Language:
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English
- Keywords:
- Pubs id:
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1147985
- Local pid:
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pubs:1147985
- Deposit date:
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2020-12-07
Terms of use
- Copyright holder:
- Association des Publications de l’Institut Henri Poincaré
- Copyright date:
- 2021
- Rights statement:
- © 2021 Association des Publications de l’Institut Henri Poincaré
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Project Euclid at: https://doi.org/10.1214/20-AIHP1131
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