Generalization of the Energy Distance by Bernstein Functions
نویسندگان
چکیده
We reprove the well-known fact that energy distance defines a metric on space of Borel probability measures Hilbert with finite first moment by new approach, analyzing behavior Gaussian kernel spaces and maximum mean discrepancy analysis. From this point view, we are able to generalize family kernels related Bernstein functions conditionally negative definite kernels. also explain what occurs $$\Vert x-y\Vert ^{a}$$ for every $$a >2$$ , describing in which circumstances it between probabilities. idea completely monotone order
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2022
ISSN: ['1572-9230', '0894-9840']
DOI: https://doi.org/10.1007/s10959-022-01167-z