Abstract Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling numerical solutions multilevel hierarchy needed to obtain efficiency gains. In this work, we show indeed also when MLMC stochastic partial differential equations (SPDE) reac...

Accidents on the road have always been a major concern in modern society. According to World Health Organization, globally traffic collisions are one of leading and fastest growing causes disability death. The present research work is conducted ten years accident data an urban environment explore analyze spatial temporal variation accidents related injuries. proposed spatiotemporal model can ma...

The aim of this paper is to extend the usual framework of SPDE with monotone coefficients to include a large class of cases with merely locally monotone coefficients. This new framework is conceptually not more involved than the classical one, but includes many more fundamental examples not included previously. Thus our main result can be applied to various types of SPDEs such as stochastic rea...

A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of elliptic diffusions where the drift has a gradient structure and the resulting SPDE is of second-order parabolic type. The present article extends this metho...

A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of elliptic diffusions where the drift has a gradient structure and the resulting SPDE is of second-order parabolic type. The present article extends this metho...

In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, tensorized evolution equation for the second moment and the covariance of the solutions of the parabolic stochastic partial differential equations is derived. Well-posedness of a space-time weak variational formulation ...

Stochastic Galerkin methods have become a significant tool for the resolution of stochastic partial differential equations (SPDE). However, they suffer from prohibitive computational times and memory requirements when dealing with large scale applications and high stochastic dimensionality. Some alternative techniques, based on the construction of suitable reduced deterministic or stochastic ba...

In the present work, we establish approximation via modulation or amplitude equations of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical $\alpha$-stable Lévy processes. We study SPDEs with a cubic nonlinearity, where deterministic is close to change stability trivial solution. The natural separation time scales this bifurcation allows us obtain an describing esse...

Stochastic partial differential equations arise as mathematical models of complex multiscale systems under random influences. Invariant manifolds often provide geometric structure for understanding stochastic dynamics. In this paper, a random invariant manifold reduction principle is proved for a class of stochastic partial differential equations. The dynamical behavior is shown to be described...

Most mathematical models contain uncertainties that may be originated from various sources such as initial and boundary conditions, geometry representation of the domain and input parameters. When these sources are expressed as random processes or random fields, partial differential equations describing the underlying models become stochastic partial differential equations (SPDEs). Stochastic m...