Probability Theory
eBook - PDF

Probability Theory

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

Probability Theory

About this book

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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.

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. ยง1 Probability spaces and the language of probability theory
  8. ยง2 Laplace experiments and conditional probabilities
  9. ยง3 Random variables: Distribution, expected value, variance, Jensenโ€™s inequality
  10. ยง4 Special distributions and their properties
  11. ยง5 Convergence of random variables and distributions
  12. Chapter II Independence
  13. ยง6 Independent events and ฯƒ-algebras
  14. ยง7 Independent random variables
  15. ยง8 Products and sums of independent random variables
  16. ยง9 Infinite products of probability spaces
  17. Chapter III Laws of Large Numbers
  18. ยง10 Posing the question
  19. ยง11 Zero-one laws
  20. ยง12 Strong Law of Large Numbers
  21. ยง13 Applications
  22. ยง14 Almost sure convergence of infinite series
  23. Chapter IV Martingales
  24. ยง15 Conditional expectations
  25. ยง16 Martingales โ€” definition and examples
  26. ยง17 Transformation via optional times
  27. ยง18 Inequalities for supermartingales
  28. ยง19 Convergence theorems
  29. ยง20 Applications
  30. Chapter V Fourier Analysis
  31. ยง21 Integration of complex-valued functions
  32. ยง22 Fourier transformation and characteristic functions
  33. ยง23 Uniqueness and Continuity Theorems
  34. ยง24 Normal distribution and independence
  35. ยง25 Differentiability of Fourier transforms
  36. ยง26 Continuous mappings into the circle
  37. Chapter VI Limit Distributions
  38. ยง27 Examples of limit theorems
  39. ยง28 The Central Limit Theorem
  40. ยง29 Infinitely divisible distributions
  41. ยง30 Gauss measures and multi-dimensional central limit theorem
  42. Chapter VII Law of the Iterated Logarithm
  43. ยง31 Posing the question and elementary preparations
  44. ยง32 Probabilistic preparations
  45. ยง33 Strassenโ€™s theorem of the iterated logarithm
  46. ยง34 Supplements
  47. Chapter VIII Construction of Stochastic Processes
  48. ยง35 Projective limits of probability measures
  49. ยง36 Kernels and semigroups of kernels
  50. ยง37 Processes with stationary and independent increments
  51. ยง38 Processes with pre-assigned path-set
  52. ยง39 Continuous modifications
  53. ยง40 Brownian motion as a stochastic process
  54. ยง41 Poisson processes
  55. ยง42 Markov processes
  56. ยง43 Gauss processes
  57. ยง44 Conditional distributions
  58. Chapter IX Brownian Motion
  59. ยง45 Brownian motion with filtration and martingales
  60. ยง46 Maximal inequalities for martingales
  61. ยง47 Behavior of Brownian paths
  62. ยง48 Examples of stochastic integrals
  63. ยง49 Optional times and optional sampling
  64. ยง50 The strong Markov property
  65. ยง51 Prospectus
  66. Bibliography
  67. Symbol Index
  68. Name Index
  69. General Index