Extending infinitely divisible distributions: An algebraic approach

David Berger

doi:10.1016/j.spl.2026.110794

June 1, 2026Statistics & Probability LettersOpen Access

Extending infinitely divisible distributions: An algebraic approach

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Key Points

The aim is to define and characterize quasi-infinite divisibility within the context of Grothendieck groups of probability measures.
Introduced an algebraic approach to the Grothendieck group of probability measures.
Defined a new notion of quasi-infinite divisibility.
Characterized moments within a specific subclass of these distributions.
Demonstrated that the Grothendieck group is divisible.
Characterized a new class of quasi-infinite divisible distributions.
Provided insights into the moments associated with these distributions.

Implication

This algebraic approach defines quasi-infinite divisibility in probability measures, highlighting new properties and moments.

Abstract

We consider the Grothendieck group extension of the monoid of probability measures and give a new definition of quasi-infinite divisibility. We characterize this class and show that the Grothendieck group itself is divisible. As an application of the new notion of quasi-infinite divisibility we characterize moments in a certain subclass.

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Cite This Study

David Berger (2026) studied this question.

synapsesocial.com/papers/6a32398fd50b63ecad20506c https://doi.org/10.1016/j.spl.2026.110794

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Extending infinitely divisible distributions: An algebraic approach

Key Points

Implication

Abstract

Discussion

Cite This Study

Extending infinitely divisible distributions: An algebraic approach

Key Points

Implication

Abstract

Discussion

Cite This Study

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