4 papers · 1 filter
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…
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…
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…
Integer-valued valuations
Andrii Ilienko, Ilya Molchanov, Tommaso Visonà
We obtain a complete characterization of planar monotone -continuous valuations taking integer values, without assuming invariance under any group of transformations. We further…