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
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.