Donsker’s fuzzy invariance principle under the Lindeberg condition
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Abstract We prove an analogue of the Donsker theorem under the Lindeberg condition in a fuzzy setting. Specifically, we consider a certain triangular system of d-dimensional fuzzy random variables { X n , i ∗ } , $\begin{array}{} \{X_{n,i}^*\}, \end{array}$ n ∈ ℕ and i = 1, 2, …, kn , which take as their values fuzzy vectors of compact and convex α-cuts. We show that an appropriately normalized and interpolated sequence of partial sums of the system may be associated with a time-continuous process defined on the unit interval t ∈ [0, 1] which, under the assumption of the Lindeberg condition, tends in distribution to a standard Brownian motion in the space of support functions.
2018 ◽
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pp. 27-42
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2001 ◽
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pp. 499-503
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1986 ◽
Vol 114
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pp. 409-422
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2013 ◽
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pp. 551
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2017 ◽
Vol 48
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pp. 3305-3315
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1994 ◽
Vol 64
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pp. 387-393
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2018 ◽
Vol 47
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pp. 53-67
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