For continuous local martingales, the total-variation process of their quadratic covariation satisfiesIt is the Cauchy-Schwarz inequality for the matrix-valued measure formed by their quadratic variations and quadratic covariation.
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The Kunita–Watanabe inequality is a result in the theory of stochastic processes, specifically concerning martingales and stochastic integrals. It provides a bound on the expected value of the square of a stochastic integral, which is an integral with respect to a martingale or a more general stochastic process.