6 papers · 1 filter
A convenient characterisation of convergent upper transition operators
Jasper De Bock, Alexander Erreygers, Floris Persiau
Motivated by its connection to the limit behaviour of imprecise Markov chains, we introduce and study the so-called convergence of upper transition operators: the condition that fo…
Randomness and imprecision: from supermartingales to randomness tests
Gert de Cooman, Floris Persiau, Jasper De Bock
We generalise the randomness test definitions in the literature for both the Martin-Löf and Schnorr randomness of a series of binary outcomes, in order to allow for interval-valued…
Imprecision in Martingale-Theoretic Prequential Randomness
Floris Persiau, Gert de Cooman
In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast `on the fly' without the need for fully specifying a probability measure on…
On the (dis)similarities between stationary imprecise and non-stationary precise uncertainty models in algorithmic randomness
Floris Persiau, Jasper De Bock, Gert de Cooman
The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of…
The Smallest Probability Interval a Sequence Is Random for: A Study for Six Types of Randomness
Floris Persiau, Jasper De Bock, Gert de Cooman
There are many randomness notions. On the classical account, many of them are about whether a given infinite binary sequence is random for some given probability. If so, this proba…
Computable randomness is about more than probabilities
Floris Persiau, Jasper De Bock, Gert de Cooman
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness i…