Small time asymptotics for Brownian motion with singular drift

2018/08/07 by Zhen-Qing Chen, Chen, Zhen-Qing, Shizan Fang +3
Economics, Econometrics and Finance · Mathematics · #35R60 #Advanced Harmonic Analysis Research #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 60H15 #Probability (math.PR) #Secondary 93E20 #Stochastic processes and financial applications #math.PR #msc:35R60 #msc:60H15 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1808.02326

arxiv created 2018/08/07 · openalex publication_date 2018/08/07 · arxiv updated 2018/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a small time large deviation principle and a Varadhan type asymptotics for Brownian motion with singular drift on \bR^d with d≥ 3 whose infinitesimal generator is \frac12 Δ+ μ⋅ ∇, where each μ_i of μ= (μ₁, ⋯, μ_d) is a measure in some suitable Kato class.

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