17 citations · 26 across the 18 of their papers we have counts for
13 papers · 1 filter
Computing lower expectations with respect to total variation distance and chi-squared divergence balls
Jasper De Bock
We derive closed form expressions for the lower expectations that correspond to total variation distance and chi-squared divergence balls around a probability mass function over a…
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…
Countable-state stochastic processes with càdlàg sample paths
Alexander Erreygers, Jasper De Bock
The Daniell-Kolmogorov Extension Theorem is a fundamental result in the theory of stochastic processes, as it allows one to construct a stochastic process with prescribed finite-di…
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…
Game-Theoretic Upper Expectations for Discrete-Time Finite-State Uncertain Processes
Natan T'Joens, Jasper De Bock, Gert de Cooman
Game-theoretic upper expectations are joint (global) probability models that mathematically describe the behaviour of uncertain processes in terms of supermartingales; capital proc…
Computable Randomness is Inherently Imprecise
Gert de Cooman, Jasper De Bock
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable rand…
Imprecise Continuous-Time Markov Chains: Efficient Computational Methods with Guaranteed Error Bounds
Alexander Erreygers, Jasper De Bock
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for th…
Efficient Computation of Updated Lower Expectations for Imprecise Continuous-Time Hidden Markov Chains
Thomas Krak, Jasper De Bock, Arno Siebes
We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random…
Independent Natural Extension for Infinite Spaces: Williams-Coherence to the Rescue
Jasper De Bock
We define the independent natural extension of two local models for the general case of infinite spaces, using both sets of desirable gambles and conditional lower previsions. In c…
Imprecise Continuous-Time Markov Chains
Thomas Krak, Jasper De Bock, Arno Siebes
Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread app…
Convergence of Imprecise Continuous-Time Markov Chains
Jasper De Bock
We study the limit behaviour of a generally non-linear ordinary differential equation whose solution is a superadditive generalisation of a stochastic matrix, and provide necessary…
A study of imprecise Markov chains: joint lower expectations and point-wise ergodic theorems
Gert de Cooman, Jasper De Bock, Stavros Lopatatzidis
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such…
Continuity of imprecise stochastic processes with respect to the pointwise convergence of monotone sequences
Jasper De Bock, Gert de Cooman
We consider the joint lower expectation of a finite-state imprecise stochastic process, defined using either the Ville-Vovk-Shafer natural extension or the Williams natural extensi…