Related papers: Approximate probabilistic verification of hybrid s…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
Inhomogeneous phase-type (IPH) distributions extend classical phase-type models by allowing transition intensities to vary over time, offering greater flexibility for modeling heavy-tailed or time-dependent absorption phenomena. We focus on…
We introduce a variant of transition systems, where activation of transitions depends on conditions of the environment and upgrades during runtime potentially create additional transitions. Using a cornerstone result in lattice theory, we…
This paper proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct…
We study planning problems where autonomous agents operate inside environments that are subject to uncertainties and not fully observable. Partially observable Markov decision processes (POMDPs) are a natural formal model to capture such…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…
Piecewise diffusion Markov processes (PDifMPs) form a versatile class of stochastic hybrid systems that combine continuous diffusion processes with discrete event-driven dynamics, enabling flexible modelling of complex real-world hybrid…
Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
In this work, we study a natural nonparametric estimator of the transition probability matrices of a finite controlled Markov chain. We consider an offline setting with a fixed dataset, collected using a so-called logging policy. We develop…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
We provide a framework to bound the probability that accumulated errors were never above a given threshold on hybrid systems. Such systems are used for example to model an aircraft or a nuclear power plant on one side and its software on…
A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
We consider here systems with piecewise linear dynamics that are periodically sampled with a given period {\tau} . At each sampling time, the mode of the system, i.e., the parameters of the linear dynamics, can be switched, according to a…
We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete…
We present a variety of results analyzing the behavior of a class of stochastic processes --- referred to as Stochastic Hybrid Systems (SHSs) --- in or near equilibrium, and determine general conditions on when the moments of the process…
This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time nonhomogeneous Markov process with a finite state space. The proposed tests are…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…