Itô Calculus

Stochastic integration, Itô's lemma, and Girsanov's theorem.


field tier

Itô Calculus. Stochastic integration, Itô’s lemma, and Girsanov’s theorem.

Foundations and canonical references

The standard treatments of itô calculus approach the subject from complementary angles. Oksendal, Stochastic Differential Equations: An Introduction with Applications (2003) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Karatzas, Brownian Motion and Stochastic Calculus (1991) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for itô calculus include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2003
    Stochastic Differential Equations: An Introduction with Applications
    oksendal-2003
  • textbook · primary · 1991
    Brownian Motion and Stochastic Calculus
    karatzas-1991, shreve-1991

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