Functional Limit Theorem Without Centering for General Shot-Noise Processes

Iksanov, Alexander; Rashytov, Bohdan

doi:10.1007/s11253-021-01917-y

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2023

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“…We state a slightly corrected version of Theorem 1 in Iksanov and Rashytov (2021). The formulation in Iksanov and Rashytov (2021) contains an extra assumption, which is omitted here.…”

Section: Auxiliary Resultsmentioning

confidence: 99%

A Limit Theorem for a Nested Infinite Occupancy Scheme in Random Environment

Braganets,

Iksanov

2023

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We investigate an infinite balls-in-boxes scheme, in which boxes are arranged in nested hierarchy and random probabilities of boxes are defined in terms of iterated fragmentation of a unit mass. Gnedin and Iksanov (2020) obtained a multivariate functional central limit theorem with centering for the cumulative occupancy counts as the number of balls becomes large. We prove a counterpart of their result, in which centering is not needed and the limit processes are not Gaussian. An application is given to the scheme generated by a residual allocation model.

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“…We state a slightly corrected version of Theorem 1 in Iksanov and Rashytov (2021). The formulation in Iksanov and Rashytov (2021) contains an extra assumption, which is omitted here.…”

Section: Auxiliary Resultsmentioning

confidence: 99%

A Limit Theorem for a Nested Infinite Occupancy Scheme in Random Environment

Braganets,

Iksanov

2023

AJS

View full text Add to dashboard Cite

show abstract

Functional Limit Theorem Without Centering for General Shot-Noise Processes

Cited by 1 publication

References 12 publications

A Limit Theorem for a Nested Infinite Occupancy Scheme in Random Environment

A Limit Theorem for a Nested Infinite Occupancy Scheme in Random Environment

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