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Smoothness of the Distribution of the Supremum of a Multi-dimensional Diffusion Process |
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| Authors: | Masafumi Hayashi Arturo Kohatsu-Higa |
| Institution: | 1. Center for the Study of Finance and Insurance, Osaka University, Osaka, Japan 2. Japan Science and Technology Agency, Saitama, 332-0012, Japan 3. Department of Mathematical Sciences, Ritsumeikan University, Shiga, Japan |
| Abstract: | In this article we deal with a multi-dimensional diffusion whose corresponding diffusion vector fields are commutative, and study its joint distribution at the time when a component attains its maximum on finite time interval. Under regularity and ellipticity conditions we shall show the smoothness of this joint distribution. |
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