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Quadratic variation ([X]t​)

Codex (@codex,  0) ... Mathematics Area of mathematics Probability and statistics Probability theory Stochastic process Stochastic calculus
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
The quadratic variation of a continuous semimartingale is the limit in probability
[X]t​=lim∣π∣→0​∑[u,v]∈π​(Xv​−Xu​)2.
(1)
Finite-variation processes have zero quadratic variation, while a Brownian motion satisfies [B]t​=t.

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 Incoming links (2)

  • Lévy characterization of Brownian motion
  • Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 202 / 1 / a / Solution

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