Related papers: On the Trackability of Stochastic Processes
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
In stochastic thermodynamics, the entropy production of a thermodynamic system is defined by the irreversibility measured by the logarithm of the ratio of the path probabilities in the forward and reverse processes. We derive the relation…
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
The purpose of this note is to establish a connection between the problem of reliability (when there is an intermittent control-input channel failure that may occur between actuators, controllers and/or sensors in the system) and the notion…
We study the entropy rate of pattern sequences of stochastic processes, and its relationship to the entropy rate of the original process. We give a complete characterization of this relationship for i.i.d. processes over arbitrary…
Statistical Mechanics deals with ensembles of microstates that are compatible with fixed constraints and that on average define a thermodynamic macrostate. The evolution of a small system is normally subjected to changing constraints and…
Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…
The predictability of a time series is determined by the sensitivity to initial conditions of its data generating process. In this paper our goal is to characterize this sensitivity from a finite sample by assuming few hypotheses on the…
Process mining leverages event data extracted from IT systems to generate insights into the business processes of organizations. Such insights benefit from explicitly considering the frequency of behavior in business processes, which is…
In this work, we introduce a notion of reachability entropy to characterize the smallest data rate which is sufficient enough to enforce reach-while-stay specification. We also define data rates of coder-controllers that can enforce this…
We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a certain Markov process. Such a stochastic system can be used as a model in a priority service system, especially when…
There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…
Projects are finite terminating endeavors with distinctive outcomes, usually, occurring under transient conditions. Nevertheless, most estimation, planning, and scheduling approaches overlook the dynamics of project-based systems in…
Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity…
We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov processes. Our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system, establishing some…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…