Conditional survival distributions of Brownian trajectories in a one dimensional Piossonian environment

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Large time annealed path measure limits for a one-dimensional Brownian motion, with possibly a small drift, moving among "soft" Poissonian traps are considered. Limits with respect to both scaled and unscaled motions are derived. The results in both cases considered here agree with those shown before for the related model with "hard" traps. The proofs follow by generalizing previous techniques which identify a large clearing empty of traps in which typically the Brownian motion is confined. What is understood then, in the cases studied, is that under the annealed measure the soft traps organize to act in effect as their hard counterparts.

Original languageEnglish (US)
Pages (from-to)169-209
Number of pages41
JournalStochastic Processes and their Applications
Volume103
Issue number2
DOIs
StatePublished - Feb 1 2003
Externally publishedYes

Fingerprint

Survival Distribution
Brownian movement
Conditional Distribution
Trap
Trajectories
Trajectory
Brownian motion
Path
Motion

Keywords

  • Brownian motion
  • Confinement
  • Obstacles
  • Soft
  • Taboo process

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Statistics and Probability

Cite this

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abstract = "Large time annealed path measure limits for a one-dimensional Brownian motion, with possibly a small drift, moving among {"}soft{"} Poissonian traps are considered. Limits with respect to both scaled and unscaled motions are derived. The results in both cases considered here agree with those shown before for the related model with {"}hard{"} traps. The proofs follow by generalizing previous techniques which identify a large clearing empty of traps in which typically the Brownian motion is confined. What is understood then, in the cases studied, is that under the annealed measure the soft traps organize to act in effect as their hard counterparts.",
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AB - Large time annealed path measure limits for a one-dimensional Brownian motion, with possibly a small drift, moving among "soft" Poissonian traps are considered. Limits with respect to both scaled and unscaled motions are derived. The results in both cases considered here agree with those shown before for the related model with "hard" traps. The proofs follow by generalizing previous techniques which identify a large clearing empty of traps in which typically the Brownian motion is confined. What is understood then, in the cases studied, is that under the annealed measure the soft traps organize to act in effect as their hard counterparts.

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KW - Taboo process

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