Hypercomplex Generalizations of Gaussian-type Measures
S.V. Ludkowski
TL;DR
This paper introduces hypercomplex Gaussian-type measures linked to high-order hyperbolic PDEs and Markov processes, analyzing their characteristic functionals and cylindrical distributions to extend Gaussian measure theory.
Contribution
It presents a novel class of hypercomplex measures generalizing Gaussian measures, connecting them with high-order PDEs and Markov processes.
Findings
Characterization of hypercomplex Gaussian-type measures
Analysis of their characteristic functionals
Study of cylindrical distributions
Abstract
The article is devoted to a new type of measures which are hypercomplex generalizations of Gaussian-type measures. The considered such measures are related with solutions of high order hyperbolic PDEs and related Markov processes. Their characteristic functionals are investigated. Cylindrical distributions of these measures are studied.
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Taxonomy
TopicsMathematical Dynamics and Fractals · advanced mathematical theories · Mathematical Control Systems and Analysis