Geodesic
Convergence of a~canonical expansion for normal fields
Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 565-572

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In the present study we consider a normal separable stochastic continuous field, and we prove the convergence of a Karhunen series with probability 1 for all parameter values. This leads in particular, to the nonrandomness of points of the discontinuity and values of the discontinuity. A criterion is presented for the convergence of the canonical expansion in a uniform norm. 
@article{MZM_1973_14_4_a14,
     author = {E. I. Ostrovskii},
     title = {Convergence of a~canonical expansion for normal fields},
     journal = {Matemati\v{c}eskie zametki},
     pages = {565--572},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a14/}
}
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E. I. Ostrovskii. Convergence of a~canonical expansion for normal fields. Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 565-572. http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a14/