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Semi-Markov models are widely used for survival analysis and reliability analysis. In general, there are two competing parameterizations and each entails its own interpretation and inference properties. On the one hand, a semi-Markov…
Supermarket models with different servers become a key in modeling resource management of stochastic networks, such as, computer networks, manufacturing systems and transportation networks. While these different servers always make analysis…
This chapter presents an introduction to Markovian modeling for the analysis of sequence data. Contrary to the deterministic approach seen in the previous sequence analysis chapters, Markovian models are probabilistic models, focusing on…
This article introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents…
Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…
We consider the task of generating draws from a Markov jump process (MJP) between two time-points at which the process is known. Resulting draws are typically termed bridges and the generation of such bridges plays a key role in…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized…
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a…
Process mining is a well-established discipline of data analysis focused on the discovery of process models from information systems' event logs. Recently, an emerging subarea of process mining, known as stochastic process discovery, has…
Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately…
In this paper, we investigate a special class of stochastic Markov processes, known as Glauber dynamics. Markov processes are importance, for example, in the study of complex systems. For this, we present the basic theory of Glauber…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation…
In this paper, we develop a more general framework of block-structured Markov processes in the queueing study of blockchain systems, which can provide analysis both for the stationary performance measures and for the sojourn times of any…
In this work, we consider a finite-state inhomogeneous-time Markov chain whose probabilities of transition from one state to another tend to decrease over time. This can be seen as a cooling of the dynamics of an underlying Markov chain. We…