Regular Densities of Invariant Measures in Hilbert Spaces

✍ Scribed by G. Daprato; J. Zabczyk

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 578 KB
• Volume: 130
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1995.1076

✦ Synopsis

We consider a nonlinear differential stochastical equation in a Hilbert space, that is, a Lipschitzian perturbation of a linear equation. We prove that, under suitable hypotheses, both equations have invariant measures (\mu) and (\mu_{0}) respectively and that (\mu) is absolutely continuous with respect to (\mu_{0}). We also give several regularity results on the density (d \mu / d \mu_{0} . \quad 1995) Academic Press. Inc.