UID:
almahu_9947367164902882
Format:
1 online resource (439 p.)
ISBN:
1-281-76757-3
,
9786611767570
,
0-08-087453-3
Series Statement:
Pure and applied mathematics ; v. 133
Content:
General theory of Markov processes
Note:
Includes indexes.
,
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
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13. Mappings of the State Space14. 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
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28. Integrability Conditions29. 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
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44. Topological Characterizations of Projections45. 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
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59. Left MF's and Exceptional Sets60. 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
,
English
Additional Edition:
ISBN 0-12-639060-6
Language:
English
