Probability Theory
eBook - PDF

Probability Theory

  1. 538 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Probability Theory

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Information

Publisher
De Gruyter
Year
2011
Print ISBN
9783110139358
eBook ISBN
9783110814668
Edition
1
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Preface
  2. Table of Contents
  3. Interdependence of chapters
  4. Notation
  5. Introduction
  6. Chapter I Basic Concepts of the Theory
  7. §1 Probability spaces and the language of probability theory
  8. §2 Laplace experiments and conditional probabilities
  9. §3 Random variables: Distribution, expected value, variance, Jensen’s inequality
  10. §4 Special distributions and their properties
  11. §5 Convergence of random variables and distributions
  12. Chapter II Independence
  13. §6 Independent events and σ-algebras
  14. §7 Independent random variables
  15. §8 Products and sums of independent random variables
  16. §9 Infinite products of probability spaces
  17. Chapter III Laws of Large Numbers
  18. §10 Posing the question
  19. §11 Zero-one laws
  20. §12 Strong Law of Large Numbers
  21. §13 Applications
  22. §14 Almost sure convergence of infinite series
  23. Chapter IV Martingales
  24. §15 Conditional expectations
  25. §16 Martingales — definition and examples
  26. §17 Transformation via optional times
  27. §18 Inequalities for supermartingales
  28. §19 Convergence theorems
  29. §20 Applications
  30. Chapter V Fourier Analysis
  31. §21 Integration of complex-valued functions
  32. §22 Fourier transformation and characteristic functions
  33. §23 Uniqueness and Continuity Theorems
  34. §24 Normal distribution and independence
  35. §25 Differentiability of Fourier transforms
  36. §26 Continuous mappings into the circle
  37. Chapter VI Limit Distributions
  38. §27 Examples of limit theorems
  39. §28 The Central Limit Theorem
  40. §29 Infinitely divisible distributions
  41. §30 Gauss measures and multi-dimensional central limit theorem
  42. Chapter VII Law of the Iterated Logarithm
  43. §31 Posing the question and elementary preparations
  44. §32 Probabilistic preparations
  45. §33 Strassen’s theorem of the iterated logarithm
  46. §34 Supplements
  47. Chapter VIII Construction of Stochastic Processes
  48. §35 Projective limits of probability measures
  49. §36 Kernels and semigroups of kernels
  50. §37 Processes with stationary and independent increments
  51. §38 Processes with pre-assigned path-set
  52. §39 Continuous modifications
  53. §40 Brownian motion as a stochastic process
  54. §41 Poisson processes
  55. §42 Markov processes
  56. §43 Gauss processes
  57. §44 Conditional distributions
  58. Chapter IX Brownian Motion
  59. §45 Brownian motion with filtration and martingales
  60. §46 Maximal inequalities for martingales
  61. §47 Behavior of Brownian paths
  62. §48 Examples of stochastic integrals
  63. §49 Optional times and optional sampling
  64. §50 The strong Markov property
  65. §51 Prospectus
  66. Bibliography
  67. Symbol Index
  68. Name Index
  69. General Index

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Yes, you can access Probability Theory by Heinz Bauer, Robert B. Burckel in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.