Related papers: Optimum Paths for Systems Subject to Internal Nois…
In this article we show a robustness theorem for controlled stochastic differential equations driven by approximations of Brownian motion. Often, Brownian motion is used as an idealized model of a diffusion where approximations such as…
In this note we consider the problem of synthesizing optimal control policies for a system from noisy datasets. We present a novel algorithm that takes as input the available dataset and, based on these inputs, computes an optimal policy…
This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in…
We propose an efficient sensitivity analysis method for a wide class of colored noise-driven interacting particle systems (IPS). Our method is based on unperturbed simulations and significantly extends the Malliavin weight sampling method…
The paper is concerned with a dissipativity theory and robust performance analysis of discrete-time stochastic systems driven by a statistically uncertain random noise. The uncertainty is quantified by the conditional relative entropy of…
We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a…
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…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
We show that in periodically driven systems, along with the delta-peak at the driving frequency, the spectral density of fluctuations displays extra features. These can be peaks or dips with height quadratic in the driving amplitude, for…
In a noisy environment, oscillations loose their coherence which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional…
Progress in experimental techniques at nanoscale made measurements of noise in molecular junctions possible. These data are important source of information not accessible through average flux measurements. Emergence of optoelectronics,…
We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…
We study the collective motion of self-propelled particles affected by the spatial-dependent noise based on the Vicsek rules. Only the particles inside the special region will affected by noise. The consideration of the spatial-dependent…
We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent…
The principle of maximum irreversible is proved to be a consequence of a stochastic order of the paths inside the phase space; indeed, the system evolves on the greatest path in the stochastic order. The result obtained is that, at the…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…
A system of coherently-driven two-level atoms is analyzed in presence of two independent stochastic perturbations: one due to collisions and a second one due to phase fluctuations of the driving field. The behaviour of the quantum…
We study the stationary probability distribution of a system driven by shot noise. We find that, both in the overdamped and underdamped regime, the coordinate distribution displays power-law singularities in its central part. For…
Thermally activated escape over a potential barrier in the presence of periodic driving is considered. By means of novel time-dependent path-integral methods we derive asymptotically exact weak-noise expressions for both the instantaneous…