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Fractal Measures and their induced Gaussian Processes
Book chapter

Fractal Measures and their induced Gaussian Processes

Palle E.T. Jorgensen and James Tian
Advances in Dimension Theory, Fractal Functions and Measures, pp.87-103
Contemporary Mathematics, v. 825, American Mathematical Society
2025
DOI: 10.1090/conm/825/16510

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Abstract

Our general theme is classes of measures and their induced Gaussian Processes. Our motivation is the class of IFS fractal measures. We outline our construction, and we prove new duality results for Gaussian processes. Two features are stressed, first the Gaussian processes presented here are indexed by general measures; and secondly, the link in the induction is a framework of reproducing kernel Hilbert spaces for this measurable category. We obtain a precise necessary and sufficient condition for equivalence of pairs of probability measures which determine the corresponding two Gaussian processes.
Random Fields generalized Ito-integration random signed measures Reproducing kernel Hilbert space (RKHS) Gaussian processes measurable category IFS fractal measures

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