Large deviation for lasso diffusion process

2016/10/01 by Dermoune, Azzouz, Es-Sebaiy, Khalifa, Ouknine, Youssef
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1610.00194

Abstract

The aim of the present paper is to extend the large deviation with discontinuous statistics studied in \citeBDE to the diffusion dx^ε = -\A^\top (A x^ε - y) + μsgn(x^ε)\dt + ε dw. The discontinuity of the drift of the diffusion discussed in \citeBDE is equal to the hyperplane \x ∈ ℝ^d: x₁=0\, however, in our case the discontinuity is more complex and is equal to the set \x ∈ ℝ^d: ∏_i=1^dx_i=0\.

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