This paper investigates a broad class of non-Gaussian measures, μ_Ψ, associated with a family of generalized Wright functions, ₘΨq. First, we study these measures in Euclidean spaces Rᵈ, then define them in an abstract nuclear triple N'. We study analyticity, invariance properties, and ergodicity under a particular group of automorphisms. Then we show the existence of an Appell system which allows the extension of the non-Gaussian Hilbert space L²(μ_Ψ) to the nuclear triple consisting of test functions' and distributions' spaces, (N)¹⊂ L²(μ_Ψ)⊂(N)μ_Ψ⁻¹. Thanks to this triple, we can study Donsker's delta as a well-defined object in the space of distributions (N)μ_Ψ⁻¹.
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Beghin et al. (2024) studied this question.
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