In this paper, we show how the Itô-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To end, will first discretize SPDE in only by utilizing finite difference methods and vectorize resulting equation exploiting its sparsity. As a benchmark, apply it case of Langevin constant coefficients, where an ...

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...

This paper concerns the homogenization problem of a parabolic equation with large, timedependent, random potentials in high dimensions d ≥ 3. Depending on the competition between temporal and spatial mixing of the randomness, the homogenization procedure turns to be different. We characterize the difference by proving the corresponding weak convergence of Brownian motion in random scenery. When...

Using the generalized variational framework, strong/weak existence and uniqueness of solutions are derived for a class distribution dependent stochastic porous media equations on general measure spaces, which also extends classical well-posedness result quasilinear SPDE to case.

We prove strong uniqueness for a parabolic SPDE involving both the solution v(t, x) and its derivative ∂xv(t, x). The familiar YamadaWatanabe method for proving strong uniqueness might encounter some difficulties here. In fact, the Yamada-Watanabe method is essentially one dimensional, and in our case there are two unknown functions, v and ∂xv. However, Pardoux and Peng’s method of backward dou...

Abstract. In this article, using DiPerna-Lions theory [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinea...

We consider conditional McKean–Vlasov stochastic differential equations (SDEs), as the ones arising in large-system limit of mean field games and particle systems with interactions when common noise is present. The time-marginals solutions to these SDEs are governed by non-linear partial (SPDEs) second order, whereas their laws satisfy Fokker–Planck on space probability measures. Our paper esta...