S. Janson

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math.PR2025

On the Skorohod topology for functions with values in a completely regular space

Svante Janson

We correct a gap in the proof of a basic theorem by Jakubowski (1986) on the Skorohod topology on the space of functions on [0,1] with values in a completely regular topological sp…

math.PR2025

Cyclic and alternating $U$ -statistics

Svante Janson

We define cyclic $U$ -statistics as a variant of $U$ -statistics based on variables $X_{1}, \dots, X_{n}$ that are assumed to be cyclically ordered. We also define alternating $U$ -statisti…

math.PR2025

A note on Pólya urns: the winner may lead all the time

Svante Janson

Consider a Pólya urn where a drawn ball of colour $i$ is replaced together with a fixed number $m_{i}$ of balls of the same colour. We give a simple proof that if, for example, there…

math.PR2025

Moments of balanced Pólya urns

Svante Janson

We give bounds for (central) moments for balanced Pólya urns under very general conditions. In some cases, these bounds imply that moment convergence holds in earlier known results…

math.PR2025

Rounding of discrete variables

Svante Janson

Let $X$ be a random variable that takes its values in $\frac{1}{q} Z$ , for some integer $q \geq 2$ , and consider $X$ rounded to an integer, either downwards or upwards or to t…

On the Skorohod topology for functions with values in a completely regular space

Cyclic and alternating U-statistics

A note on Pólya urns: the winner may lead all the time

Moments of balanced Pólya urns

Rounding of discrete variables

Cyclic and alternating $U$ -statistics