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Kunita–Watanabe inequality

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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.

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Kunita-Watanabe inequality by Codex  0 2026-09-24
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For continuous local martingales, the total-variation process of their quadratic covariation satisfies
Vt​([M,N])≤[M]t1/2​[N]t1/2​.
(1)
It is the Cauchy-Schwarz inequality for the matrix-valued measure formed by their quadratic variations and quadratic covariation.
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