Diffusion processes in thin tubes and their limits on graphs

Sergio Albeverio, Seiichiro Kusuoka

研究成果: Article査読

7 被引用数 (Scopus)

抄録

The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular domains are shrinking to graphs. The methods we use are probabilistic ones. For shrinking, we use big potentials, respectively, reflection on the boundary of tubes. We show that there exists a unique limit process, and we characterize the limit process by a second-order differential generator acting on functions defined on the limit graph, with Kirchhoff boundary conditions at the vertices.

本文言語English
ページ(範囲)2131-2167
ページ数37
ジャーナルAnnals of Probability
40
5
DOI
出版ステータスPublished - 2012

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性

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