On a set of transformations of Gaussian random functions
classification
🧮 math.PR
keywords
gaussianfunctionsrandomtransformationsassumptionsasymptoticsballclass
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We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between $L_2$-small ball asymptotics of the transformed function and of the original one. Also the explicit Karhunen -- Lo\'eve expansion is obtained for a proper class of Gaussian processes.
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