MATH 545
Introduction to Stochastic Calculus
Nicholas A. Cook
Description from DukeHub
Introduction to the theory of stochastic differential equations oriented towards topics useful in applications. Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Ito's formula, Girsanov's theorem, Feynman-Kac formula, Martingale representation theorem. Additional topics have included one dimensional boundary behavior, stochastic averaging, stochastic numerical methods. Prerequisites: Undergraduate background in real analysis (Mathematics 431) and probability (Mathematics 230 or 340).
Skills
- data and statisticsdepartment: MATH
AI-resilient: 0 of 5
- No: Physical, lab or field work
- No: Live work with people
- No: Judgment someone is accountable for
- No: A craft you practice with your hands or body
- No: Small, in-person format
The checks lean on Microsoft Research, Working with AI (2025), which found generative AI applies least to physical work and hands-on work with people. A signal, not a promise. How the score works
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