A general approach for treating the spatially extended stochastic systems with the nonlinear damping and correlations between additive and multiplicative noises is developed. Within the modified cumulant expansion method, we derive an effective Fokker-Planck equation with stationary solutions that describe the character of the ordered state. We find that the fluctuation cross-correlations lead ...

We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrödinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.

A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium equation.

This paper is concerned with estimation of functionals a latent weight function that satisfies possibly high‐dimensional multiplicative moment conditions. Main examples are stochastic discount factors in asset pricing, missing data problems, and treatment effects. We propose to estimate the by an information theoretic approach combined ℓ 1 ‐penalization technique deal conditions under sparsity....

In this paper, a simple model for analysing variability in radon concentrations in homes is tested. The approach used here involves two error components, representing additive and multiplicative errors, together with variation between-houses. We use a Bayesian approach for our analysis and apply this model to two datasets of repeat radon measurements in homes; one based on 3-month long measurem...