Related papers: Ermakov Systems with Multiplicative Noise
We propose two types of stochastic extensions of nonholonomic constraints for mechanical systems. Our approach relies on a stochastic extension of the Lagrange-d'Alembert framework. We consider in details the case of invariant nonholonomic…
In this work we investigate the phenomenon of pathwise non-uniqueness for the stochastic incompressible Euler equations with a passive tracer on the whole Euclidean space. The stochastic perturbations are interpreted as a transport noise…
In this paper, we consider the classical spin systems on unbounded lattices given by infinite-dimensional stochastic differential equations (SDEs). We assume that the stochastic forcing acts only on one particle. The other particles are not…
We develop an error mitigation method for the control-free phase estimation. We prove a theorem that under the first-order correction, the noise channels with only Hermitian Kraus operators do not change the phases of a unitary operator,…
This paper considers the strong error analysis of the Euler and fast Euler methods for nonlinear overdamped generalized Langevin equations driven by the fractional noise. The main difficulty lies in handling the interaction between the…
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic mutli-symplectic…
This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral…
This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…
The measurement of data over time and/or space is of utmost importance in a wide range of domains from engineering to physics. Devices that perform these measurements therefore need to be extremely precise to obtain correct system…
The presence of quantum noises inherent to real physical systems can strongly impact the physics in hybrid quantum circuits with local random unitaries and mid-circuit measurements. The quantum noises with a size-independent occurring…
This study addresses limited attention allocation in a stochastic linear quadratic system with multiplicative noise. Our approach enables strategic resource allocation to enhance noise estimation and improve control decisions. We provide…
We study the stochastic dynamics of a two-level quantum system interacting with a stochastic magnetic field, and a single frequency electromagnetic field, with and without making the rotating wave approximation (RWA). The transformation to…
We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of the…
The paper discusses analytical and numerical results for non-harmonic, undamped, single-well, stochastic oscillators driven by additive noises. It focuses on average kinetic, potential and total energies together with the corresponding…
We analyze the long-time behavior of numerical schemes for a class of monotone stochastic partial differential equations (SPDEs) driven by multiplicative noise. By deriving several time-independent a priori estimates for the numerical…
This paper studies Langevin equation with random damping due to multiplicative noise and its solution. Two types of multiplicative noise, namely the dichotomous noise and fractional Gaussian noise are considered. Their solutions are…
We consider the problem of estimating states and parameters in a model based on a system of coupled stochastic differential equations, based on noisy discrete-time data. Special attention is given to nonlinear dynamics and state-dependent…
In the present paper, the effect of noise intensity on stochastic parabolic equations is discussed. We focus on the effect of noise on the energy solutions of the stochastic parabolic equations. By utilising It\^o's formula and the energy…
We provide a symmetry classification of scalar stochastic equations with multiplicative noise. These equations can be integrated by means of the Kozlov procedure, by passing to symmetry adapted variables.
The non-Markovian features of three typical anomalous diffusing systems are studied by analytically solving the generalized Langevin equation directly driven by three kind of internal structured-noises: harmonic noise, harmonic velocity…