Kunita–Watanabe inequality
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In stochastic calculus, the Kunita–Watanabe inequality is a generalization of the Cauchy–Schwarz inequality to integrals of stochastic processes. It was first obtained by Hiroshi Kunita and Shinzo Watanabe and plays a fundamental role in their extension of Ito's stochastic integral to square-integrable martingales.[1]
Statement of the theorem
Let M, N be continuous local martingales and H, K measurable processes. Then
where the angled brackets indicates the quadratic variation and quadratic covariation operators. The integrals are understood in the Lebesgue–Stieltjes sense.