Foundations of Modern Probability

Kallenberg, O. (2021). Foundations of Modern Probability. Springer.

Type

Book

Intellectual base

Review or monograph

Year

2021

DOI

10.1007/978-3-030-61871-1

ISBN

9783030618704

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-3-030-61871-1

Cited by

7 citations across 7 artifacts.

Domain-specific

• Cylinder set
  • A cylinder set consists of product elements whose coordinates satisfy specified conditions at a finite collection of indices while all other coordinates remain unrestricted.
• Independent and Identically Distributed Random Variables
  • Independence says learning values of some variables supplies no probabilistic information about the others; identical distribution says the same probability law governs each coordinate.
• Martingale (probability theory)
  • … from For integrable \(Y\), the process \(X_n=\mathbb E[Y\mid\mathcal F_n]\) is a martingale with respect to the increasing information sequence. to A symmetric random walk formed from independent mean-zero integrable increments is a discrete-time martingale under its natural filtration. demonstrates that continuity.
• Natural filtration
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Probability Mass Function
  • The preserved Wikipedia revision is discovery provenance only; the identity is grounded in standard probability theory and the counting-measure formulation.
• Stationary sequence
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Sub-probability measure
  • … identity and a convenient observable transfers from A canonical example satisfies the full defining rule of Sub-probability measure with all parameters and conventions explicit. to A careful use of Sub-probability measure tests the constitutive rule and nearest confusable rather than relying on topical resemblance..

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