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Stochastic Calculus - Calculus for Random Motion

When the path itself is random: Brownian motion, the Ito integral, and the SDEs behind finance and modern diffusion models

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What you'll unlock:

  • 1. Randomness in Motion: Brownian Motion and the Wiener Process
  • 2. Why Ordinary Calculus Breaks: The Rule That dW Squared Equals dt
  • 3. The Ito Integral: Integrating Against Randomness
  • 4. Ito's Lemma: The Chain Rule for Random Functions
  • 5. Stochastic Differential Equations: Drift Plus Diffusion
  • 6. Simulating SDEs: The Euler-Maruyama Method
  • 7. From Black-Scholes to Diffusion Models: Stochastic Calculus in Finance and AI
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