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.

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.


  • Rogers, L. C. G.; Williams, D. (1987). Diffusions, Markov Processes and Martingales. II, Itô; Calculus. Cambridge University Press. p. 50. doi:10.1017/CBO9780511805141. ISBN 0-521-77593-0.