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Probability Theory

- A Comprehensive Course

Bag om Probability Theory

1 Basic Measure Theory.- 2 Independence.- 3 Generating Functions.- 4 The Integral.- 5 Moments and Laws of Large Numbers.- 6 Convergence Theorems.- 7 Lp-Spaces and the Radon-Nikodym Theorem.- 8 Conditional Expectations.- 9 Martingales.- 10 Optional Sampling Theorems.- 11 Martingale Convergence Theorems and Their Applications.- 12 Backwards Martingales and Exchangeability.- 13 Convergence of Measures.- 14 Probability Measures on Product Spaces.- 15 Characteristic Functions and the Central Limit Theorem.- 16 Infinitely Divisible Distributions.- 17 Markov Chains.- 18 Convergence of Markov Chains.- 19 Markov Chains and Electrical Networks.- 20 Ergodic Theory.- 21 Brownian Motion.- 22 Law of the Iterated Logarithm.- 23 Large Deviations.- 24 The Poisson Point Process.- 25 The It├┤ Integral.- 26 Stochastic Differential Equations.- References.- Notation Index.- Name Index.- Subject Index.

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  • Sprog:
  • Engelsk
  • ISBN:
  • 9783030564018
  • Indbinding:
  • Paperback
  • Sideantal:
  • 716
  • Udgivet:
  • 31. oktober 2020
  • Udgave:
  • 32020
  • Størrelse:
  • 236x189x42 mm.
  • Vægt:
  • 1082 g.
  • 8-11 hverdage.
  • 6. december 2024
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Beskrivelse af Probability Theory

1 Basic Measure Theory.- 2 Independence.- 3 Generating Functions.- 4 The Integral.- 5 Moments and Laws of Large Numbers.- 6 Convergence Theorems.- 7 Lp-Spaces and the Radon-Nikodym Theorem.- 8 Conditional Expectations.- 9 Martingales.- 10 Optional Sampling Theorems.- 11 Martingale Convergence Theorems and Their Applications.- 12 Backwards Martingales and Exchangeability.- 13 Convergence of Measures.- 14 Probability Measures on Product Spaces.- 15 Characteristic Functions and the Central Limit Theorem.- 16 Infinitely Divisible Distributions.- 17 Markov Chains.- 18 Convergence of Markov Chains.- 19 Markov Chains and Electrical Networks.- 20 Ergodic Theory.- 21 Brownian Motion.- 22 Law of the Iterated Logarithm.- 23 Large Deviations.- 24 The Poisson Point Process.- 25 The It├┤ Integral.- 26 Stochastic Differential Equations.- References.- Notation Index.- Name Index.- Subject Index.

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