相关论文: Stochastic effects on solution landscapes for nema…

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration…

In this paper, we study the Cauchy problem for the stochastically perturbed high-dimensional modified Euler-Poincar\'{e} system (MEP2) on the torus $\mathbb{T}^d$, $d\geq 1$. We first establish a local well-posedness framework in the sense…

Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…

Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory…

We present a novel uncertainty quantification approach for high-dimensional stochastic partial differential equations that reduces the computational cost of polynomial chaos methods by decomposing the computational domain into…

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…

We study the stochastic nonlinear Schroedinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy-critical cases. For general initial data, we prove the global existence and uniqueness of…

In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…

The predictability of turbulent flows remains a challenging problem for mathematicians, physicists, and meteorologists. In this context, we consider the 3D incompressible Navier-Stokes equations with small-scale random forcing on…

In this work, we study a non-geometrical perturbation to the stealth field, which means the background remains invariant. The stealh is homogeneous in a universe whose source is dust and demand that perturbation unchanged density. As a…

Stochastic resonance shows that under some circumstances noise can enhance the response of a system to a periodic force. While this effect has been extensively investigated theoretically and demonstrated experimentally in classical systems,…

This paper establishes strong convergence rates for the spatial finite element discretization of a two-dimensional stochastic Navier--Stokes system with transport noise and no-slip boundary conditions on a convex polygonal domain. The main…

The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…

In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…

We consider the three-dimensional magnetohydrodynamics system forced by random noise. First, for smooth solutions in the ideal case, the cross helicity remains invariant while the magnetic helicity precisely equals the initial magnetic…

This paper is concerned with the random effect of the noise dispersion for stochastic logarithmic Schr\"odinger equation emerged from the optical fibre with dispersion management. The well-posedness of the logarithmic Schr\"odinger equation…

Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a…

Speech generated by parametric synthesizers generally suffers from a typical buzziness, similar to what was encountered in old LPC-like vocoders. In order to alleviate this problem, a more suited modeling of the excitation should be…

In this note, we establish optimal lower and upper Gaussian bounds for the density of the solution to a class of stochastic integral equations driven by an additive spatially homogeneous Gaussian random field. The proof is based on the…