Diffusions under a local strong Hörmander condition. Part II: tube estimates

  title={Diffusions under a local strong H{\"o}rmander condition. Part II: tube estimates},
  author={Vlad Bally and Lucia Caramellino and Paolo Pigato},
We study lower and upper bounds for the probability that a diffusion process in R^n remains in a tube around a skeleton path up to a fixed time. We assume that the diffusion coefficients σ_1 ,. .. , σ_d may degenerate but they satisfy a strong Hormander condition involving the first order Lie brackets around the skeleton of interest. The tube is written in terms of a norm which accounts for the non-isotropic structure of the problem: in a small time δ, the diffusion process propagates with… CONTINUE READING

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