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arXiv · 1610.00194

Large deviation for lasso diffusion process

Azzouz Dermoune·Khalifa Es-Sebaiy·Youssef Ouknine
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Abstract

The aim of the present paper is to extend the large deviation with discontinuous statistics studied in \cite{BDE} to the diffusion $d\mathbf{x}^\varepsilon = -\{\mathbf{A}^\top (\mathbf{A} \mathbf{x}^\varepsilon - \mathbf{y}) + \mu sgn(\mathbf{x}^\varepsilon)\}dt + \varepsilon d\mathbf{w}$. The discontinuity of the drift of the diffusion discussed in \cite{BDE} is equal to the hyperplane $\{\mathbf{x} \in \mathbb{R}^d:\ x_1=0\}$, however, in our case the discontinuity is more complex and is equal to the set $\{\mathbf{x} \in \mathbb{R}^d:\ \prod_{i=1}^dx_i=0\}$.

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Azzouz Dermoune, Khalifa Es-Sebaiy, Youssef Ouknine. 2016-10-01. Large deviation for lasso diffusion process. https://arxiv.org/abs/1610.00194

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