We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sen...

We have discussed dynamical properties of the Tsallis entropy and the generalized Fisher information in nonextensive systems described by the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the timedependent Tsallis entropy and generalized Fisher information have been obtained with the use of the q-moment approach to the Fokker-Planck equation developed...

We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical knowledge of the multiplicative noise. For multi-bit quantizers, we derive the closed-form mean-square-error (MSE) expression for the linear minimum MSE (LMMSE) est...

We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global pathwise uniqueness and the existence of pathwise solutions. New methods are employed to deal with a special type of boundary conditions and to verify the pathwise...

We propose use of Latin Hypercube Sampling to create a synthetic data set that reproduces many of the essential features of an original data set while providing disclosure protection. The synthetic micro data can also be used to create either additive or multiplicative noise which when merged with the original data can provide disclosure protection. The technique can also be used to create hybr...

We study the stochastic behavior of fundamental time-delayed feedback systems subjected to multiplicative noise. We derive exact results for the first and second moments and the autocorrelation function. For a particular class of systems we show how the variance depends on the amplitude of the multiplicative noise. Furthermore, we identify parameter regions of stationary solutions with finite a...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...