Quadratic integration of Gaussian processes

Lin, T. F.

doi:10.1090/S0002-9939-1981-0601742-3

Quadratic integration of Gaussian processes
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by T. F. Lin PDF

Proc. Amer. Math. Soc. 81 (1981), 618-623 Request permission

Abstract:

Let $x(t),0 \leqslant t \leqslant T$, be a Gaussian process whose covariance function $R(s, t)$ satisfies certain conditions. If $G(x)$ satisfies some mild condition, then the quadratic integral ${L^2} - \lim {\sum _k}G(x({t_k}))\Delta x{({t_k})^2}$ along any sequence of paritions of $[0,T]$ whose mesh goes to zero exists. The differential rule for $x(t)$ is also derived.

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