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Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
For model-based estimation methods, the modeling that is as close to reality as possible makes a vital estimation result. In simple applications, it is sufficient to model a system with a single state space model. However, there are…
The analysis of multiple time-to-event outcomes in a randomised controlled clinical trial can be accomplished with exisiting methods. However, depending on the characteristics of the disease under investigation and the circumstances in…
In this paper, we study the stabilization of two interdependent Markov jump linear systems (MJLSs) with partial information, where the interdependency arises as the transition of the mode of one system depends on the states of the other…
A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failures: internal and those provoked by external shocks. Multiple degradation levels…
Autonomous vehicles (AV) look set to become common on our roads within the next few years. However, to achieve the final breakthrough, not only functional progress is required, but also satisfactory safety assurance must be provided. Among…
We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…
This paper develops a decision algorithm for weak bisimulation on Markov Automata (MA). For that purpose, different notions of vanishing state (a concept known from the area of Generalised Stochastic Petri Nets) are defined. Vanishing…
In a recent paper, Shah [arXiv:2502.03073] derived an explicit expression for the distribution of occupancy times for a two-state Markov chain, using a method based on enumerating sample paths. We consider here the more general problem of…
With the advent of seemingly unstructured big data, and through seamless integration of computation and physical components, cyber-physical systems (CPS) provide an innovative way to enhance safety and resiliency of transport…
Multistate models can be used to describe transitions over time across states. In the presence of interval-censored times for transitions, the likelihood is constructed using transition probabilities. Models are specified using proportional…
Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear…
Multi-stage disease histories derived from longitudinal data are becoming increasingly available as registry data and biobanks expand. Multi-state models are suitable to investigate transitions between different disease stages in presence…
We introduce a class of continuous-time bivariate phase-type distributions for modeling dependencies from common shocks. The construction uses continuous-time Markov processes that evolve identically until an internal common-shock event,…
The Markovian arrival process (MAP) has proven a versatile model for fitting dependent and non-exponential interarrival times, with a number of applications to queueing, teletraffic, reliability or finance. Despite theoretical properties of…
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…
Prognoses of Traumatic Brain Injury (TBI) outcomes are neither easily nor accurately determined from clinical indicators. This is due in part to the heterogeneity of damage inflicted to the brain, ultimately resulting in diverse and complex…
We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…
Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types…
Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…