The Structure of a Markov Chain

Chapters in this book

1. Frontmatter I
2. CONTENTS OF PROCEEDINGS VOLUMES I, II, AND III V
3. PREFACE IX
4. CONTENTS XI
5. PAUL LÉVY. 1886-1971 XV
6. Passage Problems
7. Point Processes and First Passage Problems 1
8. Limit Theorems for Random Walks with Boundaries 19
9. The Range of Random Walk 31
10. On the Law of the Iterated Logarithm for Maxima and Minima 51
11. Asymptotic Distribution of the Moment of First Crossing of a High Level by a Birth and Death Process 71
12. Markov Processes—Potential Theory
13. Martin Boundaries of Random Walks on Locally Compact Groups 87
14. The Structure of a Markov Chain 131
15. Classical Potential Theory and Brownian Motion 143
16. Logarithmic Potentials and Planar Brownian Motion 177
17. Potential Operators for Markov Processes 193
18. Markov Processes—Trajectories—Functionals
19. Approximation of Continuous Additive Functionals 213
20. Poisson Point Processes Attached to Markov Processes 225
21. Regenerative Phenomena and the Characterization of Markov Transition Probabilities 241
22. Stochastic Differential Equations and Models of Random Processes 263
23. Birth and Death of Markov Processes 295
24. Stochastic Integrals and Processes with Stationary Independent Increments 307
25. On the Support of Diffusion Processes with Applications to the Strong Maximum Principle 333
26. Diffusion Processes 361
27. Point Processes, Branching Processes
28. Random Fields of Segments and Random Mosaic on a Plane 369
29. Nonhomogeneous Poisson Fields of Random Lines with Applications to Traffic Flow 383
30. Multivariate Point Processes 401
31. On Basic Results of Point Process Theory 449
32. The Distribution of Generations and Other Aspects of the Family Structure of Branching Processes 463
33. A Method for Studying the Integral Functionals of Stochastic Processes with Applications, III 481
34. Uses of the Sojourn Time Series for the Markovian Birth Process 501
35. First Emptiness Problems in Queueing, Storage, and Traffic Theory 515
36. Kuhn-GriinType Approximations for Polymer Chain Distributions 533
37. Coverage of Generalized Chess Boards by Randomly Placed Rooks 555
38. Pressure and Helmholtz Free Energy in a Dynamic Model of a Lattice Gas 565
39. The Rate of Spatial Propagation of Simple Epidemic 579
40. Asymptotic Distribution of Eigenvalues of Random Matrices 615
41. Information and Control
42. A Priori Bounds for the Riccati Equation 645
43. Lose a Dollar or Double Your Fortune 657
44. Necessary Conditions for Discrete Parameter Stochastic Optimization Problem 667
45. Differential Games 687
46. Epsilon Entropy of Probability Distributions 699
47. AUTHOR REFERENCE INDEX 709