General Theory of Markov Processes
Published on 1. November 1988
418 pages
978-0-08-087453-1 (ISBN)
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General Theory of Markov Processes
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M. Sharpe
General Theory of Markov Processes
Book
11/1997
Academic Press
€80.47
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Content
- Front Cover
- General Theory of Markov Processes
- Copyright Page
- Contents
- Chapter I. Fundamental Hypotheses
- 1. Markov Property, Transition Functions and Entrance Laws
- 2. The First Regularity Hypothesis
- 3. The Natural Filtration
- 4. Excessive Functions and the Resolvent
- 5. The Optional and Predictable s-Algebras
- 6. The Strong Markov Property
- 7. The Second Fundamental Hypothesis
- 8. Right Processes
- 9. Existence Theorem for Ray Resolvents
- 10. Hitting Times and the Fine Topology
- Chapter II. Transformations
- 11. The Lifetime Formalisms
- 12. Killing at a Terminal Time
- 13. Mappings of the State Space
- 14. Concatenation of Processes
- 15. Cartesian Products
- 16. Space-time Processes
- 17. Completion of a Resolvent
- 18. Right Process in the Ray Topology
- 19. Realizations of Right Processes
- 20. Résumé of Notation and Hypotheses
- Chapter III. Homogeneity
- 21. Measurability and the Big Shift
- 22. Construction of Projections
- 23. Relations between the s-Algebras
- 24. Homogeneous Processes and Perfection
- 25. Co-optional and Coterminal Times
- 26. Measurability on the Future
- Chapter IV. Random Measures
- 27. Random Measures and Increasing Processes
- 28. Integrability Conditions
- 29. Shifts of Random Measures
- 30. Kernels Associated with Random Measures
- 31. Dual Projections
- 32. Integral Measurability
- 33. Characterization by Potentials
- 34. Representation of Potentials
- 35. Homogeneous Random Measures
- 36. Potential Functions and Operators
- 37. Left Potential Functions
- 38. Generating Homogeneous Random Measures
- Chapter V. Ray-Knight Methods
- 39. The Ray Space
- 40. The Entrance Space
- 41. Meager Sets and Predictable Functions
- 42. Left Limits and Predictable Projections
- 43. The Predictable Projection Kernel
- 44. Topological Characterizations of Projections
- 45. Accessibility
- 46. Left Limits in the Original Topology
- 47. Quasi-Left-Continuity
- 48. Natural Processes
- 49. Balayage of Functions
- Chapter VI. Stochastic Calculus
- 50. Local Martingales over a Right Process
- 51. Decomposition Theorems
- 52. Semimartingales and Stochastic Integrals
- 53. Finite Lifetime Considerations
- Chapter VII: Multiplicative Functionals
- 54. Multiplicative Functionals and Terminal Times
- 55. Exact Perfection of a Weak MF
- 56. Exactly Subordinate Semigroups
- 57. Decreasing MF's
- 58. m-Additivity
- 59. Left MF's and Exceptional Sets
- 60. Measurability of a MF
- 61. Subprocess Generated by a Decreasing MF
- 62. Subprocess Generated by a Supermartingale MF
- Chapter VIII. Additive Functionals
- 63. Classification of Additive Functionals
- 64. Fine Support
- 65. Time Change by the Inverse of an AF
- 66. Absolute Continuity
- 67. Balayage of an AF
- 68. Local Times
- 69. Additive Functionals of Subprocesses
- 70. Relative Predictable Projections
- 71. Exponential Formulas
- 72. Two Motivating Examples
- 73. Lévy Systems
- 74. Excursions from a Homogeneous Set
- 75. Characteristic Measures of an AF
- Appendices
- A0. Monotone Class Theorems
- A1. Universal Completion and Trace
- A2. Radon Spaces
- A3. Kernels
- A4. Lebesgue-Stieltjes Integrals
- A5. Sketch of the General Theory of Processes
- A6. Relative Martingales and Projections
- References
- Notation Index
- Subject Index
- Pure and Applied Mathematics
