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We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
We study entanglement dynamics in the presence of correlated environmental noises. Specifically, we investigate the quantum entanglement dynamics of two spins in the presence of correlated classical white noises, deriving Markov master…
Using a microscopic model for stochastic transport through a single quantum dot that is modified by the Coulomb interaction of environmental (weakly coupled) quantum dots, we derive generic properties of the full counting statistics for…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
In this paper, we develop a method to model and estimate several, _dependent_ count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of…
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with…
This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered:…
Understanding the cause of the synchronization of population evolution is an important issue for ecological improvement. Here we present a Lotka-Volterra-type model driven by two correlated environmental noises and show, via theoretical…
The ubiquitous effects of the environment on quantum-mechanical systems generally cause temporally correlated fluctuations. This particularly holds for systems of interest for quantum computation where such effects lead to correlated…
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…
We propose an infinitesimal dispersion index for Markov counting processes. We show that, under standard moment existence conditions, a process is infinitesimally (over-) equi-dispersed if, and only if, it is simple (compound), i.e. it…
Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on {\em analytically-solvable}…
We study the estimation of moments and joint moments of microstructure noise. Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide…
This paper introduces a novel methodology for the identification of switching dynamics for switched autoregressive linear models. Switching behavior is assumed to follow a Markov model. The system's outputs are contaminated by possibly…
The study of noise assisted transport in quantum systems is essential in a wide range of applications from near-term NISQ devices to models for quantum biology. Here, we study a generalised XXZ model in the presence of stochastic collision…
We investigate dynamics of recurrent neural networks with correlated noise to analyze the noise's effect. The mechanism of correlated firing has been analyzed in various models, but its functional roles have not been discussed in sufficient…
This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…
A spatially extended Lotka-Volterra system of two competing species in the presence of two correlated noise sources is analyzed: (i) an external multiplicative time correlated noise, which mimics the interaction between the system and the…
In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…
We consider transitions to chaos in random dynamical systems induced by an increase of noise amplitude. We show how the emergence of chaos (indicated by a positive Lyapunov exponent) in a logistic map with bounded additive noise can be…