Absolute continuity of the laws of a multi-dimensional stochastic differential equation with coefficients dependent on the maximum

研究成果: Article

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In this article, we consider an m-dimensional stochastic differential equation with coefficients which depend on the maximum of the solution. First, we prove the absolute continuity of the law of the solution. Then we prove that the joint law of the maximum of the ith component of the solution and the i 'th component of the solution is absolutely continuous with respect to the Lebesgue measure in a particular case. The main tool to prove the absolute continuity of the laws is Malliavin calculus.

元の言語English
ページ(範囲)2499-2506
ページ数8
ジャーナルStatistics and Probability Letters
83
発行部数11
DOI
出版物ステータスPublished - 2013 11 1

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ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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