Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case

Martin Kolb; Mladen Savov

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arXiv · 1405.4439

Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case

Martin Kolb·Mladen Savov

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Abstract

In this work we consider a one-dimensional Brownian motion with constant drift moving among a Poissonian cloud of obstacles. Our main result proves convergence of the law of processes conditional on survival up to time $t$ as $t$ converges to infinity in the critical case where the drift coincides with the intensity of the Poisson process. The complements a previous result of T. Povel, who considered the same question in the case where the drift is strictly smaller than the intensity.

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Martin Kolb, Mladen Savov. 2015-03-07. Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case. https://arxiv.org/abs/1405.4439

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