Singularity of generalized grey Brownian motions with different parameters
Jos\'e Lu\'is da Silva, Mohamed Erraoui
TL;DR
This paper proves that generalized grey Brownian motions with different parameters generate mutually singular probability measures, extending the Feldman-Hájek dichotomy from Gaussian to non-Gaussian measures.
Contribution
It establishes the singularity of measures generated by different parameterized generalized grey Brownian motions, extending classical Gaussian measure results.
Findings
Measures are mutually singular for different parameters
Extension of Feldman-Hájek dichotomy to non-Gaussian measures
Provides a foundation for understanding non-Gaussian stochastic processes
Abstract
In this note we prove that the probability measures generated by two generalized grey Brownian motions with different parameters are singular with respect to each other. This result can be interpreted as an extension of the Feldman-H\'ajek dichotomy of Gaussian measures to a family of non-Gaussian measures
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