Smooth densities of the laws of perturbed diffusion processes

Lihu Xu, Wen Yue, Tusheng Zhang

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Under some regularity conditions on b, σ and α, we prove that the solution of the following perturbed stochastic differential equation Xt=x+∫0 tb(Xs)ds+∫0 tσ(Xs)dBs+αsup0≤s≤tXs,α0, where t0>0 is some finite number.

Original languageEnglish
Pages (from-to)55-62
Number of pages8
JournalStatistics and Probability Letters
Early online date25 Jul 2016
Publication statusPublished - 1 Dec 2016


  • Malliavin differentiability
  • Perturbed diffusion processes
  • Smooth density


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