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math.PR2025
Ranges of Extremal Processes and Heavy-Tailed Random Walks in Spaces of Growing Dimension
Bochen Jin, Ilya Molchanov
We consider extremal processes and random walks generated by heavy-tailed random vectors taking values in endowed with the metric. We establish limit theor…
math.PR2025
Set-valued conditional functionals of random sets
Tobias Fissler, Ilya Molchanov
Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variab…
math.PR2025
Foundations of regular variation on topological spaces
Bojan Basrak, Nikolina Milinčević, Ilya Molchanov
Since its introduction by J. Karamata, regular variation has evolved from a purely mathematical concept into a cornerstone of theoretical probability and data analysis. It is exten…