2019/05/14 by Alexander Erreygers, Erreygers, Alexander, Jasper De Bock +1
Computer Science · Decision Sciences · #Bayesian Modeling and Causal Inference #FOS: Mathematics #Formal Methods in Verification #Probability (math.PR) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1905.05734
openalex publication_date 2019/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here consider a rate interval and let it characterise two nested sets of stochastic processes. We call these two sets of stochastic process imprecise Poisson processes, explain why this is justified, and study the corresponding lower and upper (conditional) expectations. Besides a general theoretical framework, we also provide practical methods to compute lower and upper (conditional) expectations of functions that depend on the number of events at a single point in time.