Generators of Markov chains : from a walk in the interior to a dance on the boundary

Contents
Preface
A Nontechnical Introduction
1 A Guided Tour through the Land of Operator Semigroups
	1.1 Semigroups and Generators
	1.2 The Hille–Yosida Theorem
	1.3 Perturbation Theorems
	1.4 Approximation and Convergence Theorems
	1.5 Dual and Sun-Dual Semigroups
	1.6 Appendix: On Convergence in l1
	1.7 Notes
2 Generators versus Intensity Matrices
	2.1 Transition Matrices and Markov Operators in l1
	2.2 The Matrix of Intensities
	2.3 The Uniform Case
	2.4 The Generator
	2.5 Intensities, Generators, and Infinitesimal Description
	2.6 Back to the First Kolmogorov–Kendall–Reuter Example
	2.7 Back to the Second Kolmogorov–Kendall–Reuter Example
	2.8 Blackwell’s Example
	2.9 Notes
3 Boundary Theory: Core Results
	3.1 Kato’s Theorem
	3.2 The Question of Explosiveness
	3.3 Pure Birth Process Example
	3.4 On the Domain of the Minimal Semigroup Generator
	3.5 Beyond Kato’s Theorem
	3.6 Close to the Edge: Lattice B
	3.7 The (Discrete, Exit) Boundary
	3.8 More on Extremal and Minimal Functionals
	3.9 Notes
4 Boundary Theory Continued
	4.1 Sojourn Sets and Sojourn Solutions
	4.2 A Broader Perspective
	4.3 P. Lévy’s Flash
	4.4 The Joy of Entrance Laws
	4.5 Notes
5 The Dual Perspective
	5.1 Preliminaries
	5.2 Markov Chains with Feller Property
	5.3 Generators of Feller Semigroups
	5.4 More on Feller Semigroups
	5.5 The Feynman–Kac and the Volkonskii Formulae
	5.6 Kolmogorov, Kendall, and Reuter Revisited
	5.7 Sun-Duals of Nonminimal Processes: A Case Study
	5.8 Can We Generalize?
	5.9 Calling on P. Lévy Again
	5.10 Notes
Solutions and Hints to Selected Exercises
Commonly Used Notation
References
Index