Smooth densities of the laws of perturbed diffusion processes

2016/01/23 by Lihu Xu, Xu, Lihu, Wen Yue +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #60H07 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60H07

paper · pdf · doi:10.48550/arxiv.1601.06275

arxiv created 2016/01/23 · openalex publication_date 2016/01/23 · arxiv updated 2016/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under some regularity conditions on b, σ and α, we prove that the following perturbed stochastic differential equation X_t=x+∫₀^t b(X_s)ds+∫₀^t σ(X_s) dB_s+αsup_{0 ≤ s ≤ t} X_s, α<1 admits smooth densities for all 0 ≤ t ≤ t₀, where t₀>0 is some finite number.

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