Resolvent Estimates for Fleming–Viot Operators with Brownian Drift

✍ Scribed by Peter March

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 298 KB
• Volume: 160
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1998.3290

✦ Synopsis

This article is a supplement to the paper of D. A. Dawson and P. March (J. Funct. Anal. 132 (1995), 417 472). We define a two-parameter scale of Banach spaces of functions defined on M 1 (R d ), the space of probability measures on d-dimensional euclidean space, using weighted sums of the classical Sobolev norms. We prove that the resolvent of the Fleming Viot operator with constant diffusion coefficient and Brownian drift acts boundedly between certain members of the scale. These estimates gauge the degree of smoothing performed by the resolvent and separate the contribution due to the diffusion coefficient and that due to the drift coefficient.