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The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information…

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…

In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations…

The archetypal system demonstrating stochastic resonance is nothing more than a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a…

In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

So far it has been shown that the quantum dynamics cannot be described as a classical Markov process unless the number of classical states is uncountably infinite. In this paper, we present a stochastic model with time-correlated noise that…

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

We study the stationary states of variants of the noisy voter model, subject to fluctuating parameters or external environments. Specifically, we consider scenarios in which the herding-to-noise ratio switches randomly and on different time…

Stochastic optimization is a vital field in the realm of mathematical optimization, finding applications in diverse areas ranging from operations research to machine learning. In this paper, we introduce a novel first-order optimization…

We establish a quantum functional central limit for the dynamics of a system coupled to a Fermionic bath with a general interaction linear in the creation, annihilation and scattering of the bath reservoir. Following a quantum Markovian…

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…

This work deals with the dynamics of a class of stochastic dynamical systems with a multiplicative non-Gaussian Levy noise. We first establish the existence of stable and unstable foliations for this system via the Lyapunov-Perron method.…

Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…

Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

This paper studies the spectrum assignment of a class of stochastic systems with multiplicative noise. A novel $\alpha$-spectrum assignment is proposed for discrete-time and continuous-time stochastic systems with multiplicative noise. In…

We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…

Quantum stochastic processes are widely used in describing open quantum systems and in the context of quantum foundations. Physically relevant quantum stochastic processes driven by multiplicative colored noise are generically non-Markovian…