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Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here…
We address the general problem of formulating the dynamical large deviations of non-Markovian systems in a closed form. Specifically, we consider a broad class of ``self-interacting'' jump processes whose dynamics depends on the past…
We generalize the notion of Gaussian bridges by conditioning Gaussian processes given that certain linear functionals of the sample paths vanish. We show the equivalence of the laws of the unconditioned and the conditioned process and by an…
We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized Langevin equation, in which we expand the…
In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles…
We introduce a class of Markov processes conditioned to avoid intersection over a moving time window of length T>0, a setting we refer to as myopic non-intersection. In particular, we study a system of myopic non-intersecting Brownian…
In this study, we address the central issue of statistical inference for Markov jump processes using discrete time observations. The primary problem at hand is to accurately estimate the infinitesimal generator of a Markov jump process, a…
Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received an increasing attention during the last decades, thanks to the information…
This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identification failures that plague conventional likelihood-based…
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…
A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not…
Non-Markovian effects in open quantum system dynamics usually manifest backflow of information from the environment to the system, indicating complete-positive divisibility breaking of the dynamics. We provide a criterion for witnessing…
We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…
In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation…
We introduce an infinite time horizon Brownian bridge which is determined by a stochastic Langevin equation with time dependent drift coefficient. We show that this process goes to zero almost surely when the time goes to infinity and study…
The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and…
We consider a system of $N$ non-crossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we…
For classical Markovian stochastic systems, past and future events become statistically independent when conditioned to a given state at the present time. Memory non-Markovian effects break this condition, inducing a non-vanishing…
The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of non-stationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred…
This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time T > 0…