• Corpus ID: 27555044

The frog model with drift on R

@article{Rosenberg2016TheFM,
  title={The frog model with drift on R},
  author={Josh Rosenberg},
  journal={arXiv: Probability},
  year={2016}
}
  • J. Rosenberg
  • Published 26 May 2016
  • Mathematics
  • arXiv: Probability
Consider a Poisson process on $\mathbb{R}$ with intensity $f$ where $0 \leq f(x)<\infty$ for ${x}\geq 0$ and ${f(x)}=0$ for $x<0$. The "points" of the process represent sleeping frogs. In addition, there is one active frog initially located at the origin. At time ${t}=0$ this frog begins performing Brownian motion with leftward drift $\lambda$ (i.e. its motion is a random process of the form ${B}_{t}-\lambda {t}$). Any time an active frog arrives at a point where a sleeping frog is residing… 
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