Related papers: Large Deviations in Safety-Critical Systems with P…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…
In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme…
Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such…
We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple…
We estimate the initial conditions of a multivariable dynamical system from a scalar signal, using a modified Newton-Raphson method incorporating the time evolution. We can estimate initial conditions of periodic and chaotic systems and the…
We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is…
Assuring safety in discrete time stochastic hybrid systems is particularly difficult when only noisy or incomplete observations of the state are available. We first review a formulation of the probabilistic safety problem under noisy hybrid…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting particles indexed by a lattice $\mathbb{Z}^d$. The connections are random, sparse and unscaled, so that the system converges in the large…
The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction…
The safety concern for unmanned systems, namely the concern for the potential casualty caused by system abnormalities, has been a bottleneck for their development, especially in populated areas. Evidently, the collision between the unmanned…
We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system…
We propose and compare methods for the analysis of extreme events in complex systems governed by PDEs that involve random parameters, in situations where we are interested in quantifying the probability that a scalar function of the…
We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.
The complexity of the operating environment and required technologies for highly automated driving is unprecedented. A different type of threat to safe operation besides the fault-error-failure model by Laprie et al. arises in the form of…