Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Quadratic Variation

Chapter 19 Dynamics & diffusion

Chapter 19: Stochastic Differential Equations — Quadratic Variation

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Quadratic Variation — animated GIF preview
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Quadratic Variation — high-resolution mind-map icon

From the book

Chapter 19: Stochastic Differential Equations. In the chapter mind map this icon labels Quadratic Variation. The discussion below is excerpted and lightly edited from § Quadratic Variation in Mathematics for AI and Machine Learning.

Itô calculus, SDEs, and continuous-time stochastic processes

What this drawing shows

What you see. Identity $(dW_t)^2 = dt$ fixed; purple area and $dt$ / $dW$ legs grow to show quadratic variation equals the time increment.

In the mind map. Chapter 19 — Quadratic Variation. See From the book above for definitions, figures, and worked examples.

Where to read next

Open Chapter 19 companion →

Read the full definitions, figures, and worked examples in Chapter 19: Stochastic Differential Equations — see the mind-map node Quadratic Variation.