A simple method for finite range decomposition of quadratic forms and Gaussian fields

• 成果类型: Article
• 署名作者: Bauerschmidt, Roland
• 署名单位: University of British Columbia
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0471-y
• 发表日期: 2013
• 页码: 817-845
• 关键词: positive-definite functions; fundamental-solutions; parabolic-systems; MARKOV-PROCESSES; chains

摘要

We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are smoother than the original Green form. This result gives rise to multiscale decompositions of the associated Gaussian free fields into sums of independent smoother Gaussian fields with spatially localized correlations. Our method makes use of the finite propagation speed of the wave equation and Chebyshev polynomials. It improves several existing results and also gives simpler proofs.