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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quadratic integration of Gaussian processes


Author: T. F. Lin
Journal: Proc. Amer. Math. Soc. 81 (1981), 618-623
MSC: Primary 60G15
DOI: https://doi.org/10.1090/S0002-9939-1981-0601742-3
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.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0601742-3
Keywords: Gaussian process, covariance function, quadratic integral, Ito's formula
Article copyright: © Copyright 1981 American Mathematical Society