In this paper we present the theoretical framework needed to justify the use of a kernelbased collocation method (meshfree approximation method) to estimate the solution of highdimensional stochastic partial differential equations (SPDEs). Using an implicit time stepping scheme, we transform stochastic parabolic equations into stochastic elliptic equations. Our main attention is concentrated on...

Traffic deaths and injuries are one of the major global public health concerns. The present study considers accident records in an urban environment to explore analyze spatial temporal incidence road traffic accidents. We propose a spatio-temporal model provide predictions number collisions on any given segment, further generate risk map entire network. A Bayesian methodology using Integrated n...

in this article,we present a wavelet method for solving stochastic volterra integral equations based on haar wavelets. first, we approximate all functions involved in the problem by haar wavelets then, by substituting the obtained approximations in the problem, using the it^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion coefficients. Under certain type of Lipschitz and linear growth conditions, we develop a method to prove the existence and uniqueness of adapted solution to the...

In this paper a control problem for a controlled linear stochastic equation in a Hilbert space and an exponential quadratic cost functional of the state and the control is formulated and solved. The stochastic equation can model a variety of stochastic partial differential equations with the control restricted to the boundary or to discrete points in the domain. The solution method does not req...

A new method is proposed for modelling the yearly maxima of sub-daily precipitation, with aim producing spatial maps return level estimates. Yearly precipitation are modelled using a Bayesian hierarchical model latent Gaussian field, blended generalised extreme value (bGEV) distribution used as substitute more standard (GEV) distribution. Inference made less wasteful novel two-step procedure th...

We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection diffusion reaction partial differential equation and a spatially distributed stochastic lattice noise model. The stochastic dynamics include both spin-flip and spin-exchange type inter-particle interactions. Furthermore, we consider a new, asymmetric, single exclusion process, studied elsew...

We consider a numerical solution of the stochastic moving boundary value problem, whose existence and uniqueness of solution are proved in [16]. Numerical approximations are based on the transformation which transforms the stochastic moving boundary problem whose spatial domain is a priori unknown to a nonlinear stochastic partial differential equation which has a fixed spatial domain. We const...