Probability with Martingales

Williams, D. (1991). Probability with Martingales. Cambridge University Press.

Type

Book

Intellectual base

Review or monograph

Year

1991

DOI

10.1017/cbo9780511813658

ISBN

9780521404556

Link

https://www.cambridge.org/highereducation/books/probability-with-martingales/B4CFCE0D08930FB46C6E93E775503926

Cited from

mathematics

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Conditional Probability
  • Statistics and probability theory. The foundational object on which inference, decision theory, and stochastic-process theory are built; the filtration of information in martingale theory is the continuous-time generalization of conditioning.

    This sourceStandard text developing conditional expectation and filtrations, the continuous-time generalization of conditioning on accumulated information in martingale theory.

• Stochastic Process
  • The martingale concept transfers from gambling and fair games to the no-arbitrage pricing of derivatives (a discounted price is a martingale under the risk-neutral measure) to the analysis of stochastic algorithms (martingale concentration bounds), because "the conditional future expectation equals the present" is a substrate-free structural property.

    This sourceCanonical treatment of martingales — conditional future expectation equal to the present — as a substrate-free structural property.

Domain-specific

• Doob Decomposition Theorem
  • Williams states this discrete-time decomposition and its uniqueness in the martingale-theory development of Probability with Martingales.
• Doob martingale
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Martingale (probability theory)
  • The entry states the probability-theoretic object; financial fair-price interpretations require a chosen measure, numeraire, admissibility assumptions, and no-arbitrage framework.

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Links previously used in the corpus

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• https://doi.org/10.1017/CBO9780511813658 ×2

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