Theoretical analysis demonstrates quasi-translation invariance for generalized grey Brownian motions, highlighting gradient operator closability in non-Gaussian measures.
In this article, we study the quasi-translation-invariant property of a class of non-Gaussian measures. These measures are associated with the family of generalized grey Brownian motions. We identify the Cameron–Martin space and derive the explicit Radon-Nikodym density in terms of the Wiener integral with respect to the fractional Brownian motion. Moreover, we show an integration by parts formula for the derivative operator in the directions of the Cameron–Martin space. As a consequence, we derive the closability of both the derivative and the corresponding gradient operators.
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Silva et al. (2024) studied this question.
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