Plane Wave Decomposition of Even-Dimensional Brownian Local Times

✍ Scribed by Hideaki Uemura

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 154 KB
• Volume: 173
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3566

✦ Synopsis

We study the one-dimensional representations of even-dimensional Brownian local time in two ways. The first result is obtained by the application of the odddimensional case. The second is led by the plane wave decomposition of the $-function. The Hilbert transform of derivatives of local time is considered in the second result, in which Hermite functions of the second kind appear in the kernel of the Wiener Ito^decomposition.