Kunita–Watanabe theorem

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In stochastic calculus, the Kunita–Watanabe theorem or Kunita-Watanabe inequality is a generalization of the Cauchy Schwarz inequality to integrals of stochastic processes.

Statement of the Theorem[edit]

Let M, N be continuous local martingales and H,K measurable processes. Then

Where the brackets indicates the quadratic variation and quadratic covariation operators. The integrals are understood in the Lebesgue-Stieltjes sense.