Related papers: Markovian Statistics on Evolving Systems
What can one infer about the dynamical evolution of quantum systems just by symmetry considerations? For Markovian dynamics in finite dimensions, we present a simple construction that assigns to each symmetry of the generator a family of…
Motivated by the dynamic modeling of relative abundance data in ecology, we introduce a general approach to model stationary Markovian or non Markovian time series on (relatively) compact spaces such as a hypercube, the simplex or a sphere…
In the present work we study Bayesian nonparametric inference for the continuous-time M/G/1 queueing system. In the focus of the study is the unobservable service time distribution. We assume that the only available data of the system are…
We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…
Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the…
When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics…
Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating…
Multivariate regression models and ANOVA are probably the most frequently applied methods of all statistical analyses. We study the case where the predictors are qualitative variables, and the response variable is quantitative. In this…
We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…
Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a…
We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for…
We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each…
Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. In this paper, we develop a theoretical large…
We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we…
We consider a class of open quantum many-body Lindblad dynamics characterized by an all-to-all coupling Hamiltonian and by dissipation featuring collective ``state-dependent" rates. The latter encodes local incoherent transitions that…