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Proceedings of the American Mathematical Society

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Quadratic integration of Gaussian processes

Author: T. F. Lin
Journal: Proc. Amer. Math. Soc. 81 (1981), 618-623
MSC: Primary 60G15
MathSciNet review: 601742
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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.

References [Enhancements On Off] (What's this?)

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Keywords: Gaussian process, covariance function, quadratic integral, Ito's formula
Article copyright: © Copyright 1981 American Mathematical Society

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