Article ID Journal Published Year Pages File Type
1151693 Statistics & Probability Letters 2013 8 Pages PDF
Abstract

In this article, we consider an mm-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 iith component of the solution and the i′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.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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