9 citations · 14 across the 12 of their papers we have counts for
19 papers
C{à}dl{à}guity and compactness in submetric spaces
Adam Jakubowski
A submetric space is a topological space equipped with a continuous metric that generates a metric topology weaker than the original one (e.g., a separable Hilbert space with the w…
A complement to the Chebyshev integral inequality
Adam Jakubowski
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
Directional phantom distribution functions for~stationary random fields
Adam Jakubowski, Igor Rodionov, Natalia Soja-Kukieła
We give necessary and sufficient conditions for the existence of a phantom distribution function for a stationary random field on a regular lattice. We also introduce a less demand…
Truncated moments of perpetuities and a new central limit theorem for GARCH processes without Kesten's regularity
Adam Jakubowski, Zbigniew S. Szewczak
We consider a class of perpetuities which admit direct characterization of asymptotics of the key truncated moment. The class contains perpetuities without polynomial decay of tail…
Stable limits for associated regularly varying sequences
Adam Jakubowski
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponen…
Stable limits for Markov chains via the Principle of Conditioning
Mohamed El Machkouri, Adam Jakubowski, Dalibor Volný
We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable…