Related papers: Systems with Multiplicative Noise: Critical Behavi…
We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…
We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first…
Dynamical phase transitions are nonequilibrium counterparts of thermodynamic phase transitions and share many similarities with their equilibrium analogs. In continuous phase transitions, critical exponents play a key role in characterizing…
We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…
In this paper, the consensus problems of the continuous-time integrator systems under noisy measurements are considered. The measurement noises, which appear when agents measure their neighbors' states, are modeled to be multiplicative. By…
Critical exponents have been obtained for a 3D spin particle system. Clusters are formed and system reaches a critical behavior when fragment size distribution follows a power law, as predicted by Fisher Liquid Droplet Model. Also,…
We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…
We present a dynamical and dissipative lattice model, designed to mimic nuclear multifragmentation. Monte-Carlo simulations with this model show clear signature of critical behaviour and reproduce experimentally observed correlations. In…
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
The influence of outside quantum noises on the amplification of weak measurements is investigated. Three typical quantum noises are discussed. The maximum values of the pointer's shifts decrease sharply with the strength of the depolarizing…
An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…
Physical situations involving multiplicative noise arise generically in cosmology and field theory. In this paper, the focus is first on exact nonlinear Langevin equations, appropriate in a cosmologica setting, for a system with one degree…
We propose a policy iteration algorithm for solving the multiplicative noise linear quadratic output feedback design problem. The algorithm solves a set of coupled Riccati equations for estimation and control arising from a partially…
State estimators are crucial components of anomaly detectors that are used to monitor cyber-physical systems. Many frequently-used state estimators are susceptible to model risk as they rely critically on the availability of an accurate…
The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…
Quantum critical systems with multiple dynamics possess not only one but several time scales, tau_i ~ xi^(z_i), which diverge with the correlation length xi. We investigate how scaling predictions are modified for the simplest case of…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science, and applied mathematics. This paper characterizes the behavior of perturbed eigenvectors for a range of…
This paper is devoted to proving the small noise asymptotic behaviour, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main…