Itô's Formula

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External reading guide · Graduate

Applying a smooth function to Brownian motion introduces a second-derivative correction absent from ordinary calculus. Work through the square-function example to connect that correction with quadratic variation.

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Brownian Motion · Martingale · second derivative

Where to read

  1. Start here: Probability: Theory and Examples (Version 5)

    Rick Durrett · Book · English · Free full text

    §7.6 Itô's formula, Theorem 7.6.1 and Example 7.6.3

    Checked 2026-10-16

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