Hyperfinite Dirichlet Forms

Abstract

The interplay between methods from functional analysis and the theory of stochastic processes is one of the most important and exciting aspects of mathematical physics today. It is a highly technical and sophisticated theory based on decades of research in both areas. Numerous papers have been writ- ten on the standard theory of Dirichlet forms. Apart from the articles and monographs cited below, other notable contributions to the area include: Albeverio and Bernabei [4], Albeverio et al. [31], Bliedtner [85], Bouleau [89], Bouleau and Hirsch [90], Chen et al. [103], Fabes, Fukushima, Gross, Kenig, RÖckner and Stroock [144], Fitzsimmons and Kuwae [163], Fukushima [168– 170], Fukushima and Tanaka [176], Fukushima and Ying [179,180], Grothaus et al. [189], Hesse et al. [198], Jacob [208–210], Jacob and Moroz [211], Jacob and Schilling [212], Jost et al. [214], Kassmann [221], Kim et al. [229], Kumagai and Sturm [237], Ma and RÖckner [261,262], Ma et al. [263], Oshima [283], RÖckner and Wang [304], RÖckner and Zhang [306], Schmuland and Sun [316], Shiozawa and Takeda [318], da Silva et al. [319], Stannat [325], and Takeda [333, 334].