6 papers
Foundations of regular variation on topological spaces
Bojan Basrak, Nikolina MilinÄeviÄ, 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…
Set-indexed and multiple sums in high dimensions
Bochen Jin, Alexander Marynych, Ilya Molchanov
We consider multiple and set-indexed sums of random vectors taking values in Euclidean space of growing dimension. It is shown that, when viewed as finite metric spaces, the sets o…
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 theore…
Integer-valued valuations
Andrii Ilienko, Ilya Molchanov, Tommaso VisonÃ
We obtain a complete characterization of planar monotone -continuous valuations taking integer values, without assuming invariance under any group of transformations. We furthe…
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…
Set-valued recursions arising from vantage-point trees
Congzao Dong, Alexander Marynych, Ilya Molchanov
We study vantage-point trees constructed using an independent sample from the uniform distribution on a fixed convex body in , where is an…