Huang, Xueping: On stochastic completeness of weighted graphs. 2011
Inhalt
- Preface
- 0 Introduction
- 1 Foundations
- 1.1 Weighted graphs
- 1.2 Dirichlet forms, semigroups and resolvents
- 1.3 Minimum principles
- 1.4 Dirichlet subgraphs
- 1.5 The equivalence theorem
- 1.6 The graph distance and adapted distances
- 1.7 Continuous time Markov chains
- 2 The weak Omori-Yau maximum principle
- 2.1 Equivalence to stochastic completeness
- 2.2 A key lemma
- 2.3 Khas'minskii criterion
- 2.4 Stability of stochastic incompleteness
- 2.5 Applications to the physical Laplacian
- 3 Uniqueness class
- 4 Stochastic completeness and volume growth
- 4.1 Volume growth criteria in the adapted distances
- 4.2 Volume growth criteria in the graph distance
- 4.3 Examples
- 5 Escape rate
- 5.1 Main strategy
- 5.2 Exit time estimate
- 5.3 Upper rate function for case (1)
- 5.4 Upper rate function for case (2)
- Bibliography
- Notation