Motivated by the meteorological question whether a turbulent velocity field accelerates rain droplets merging and favors rain, we prove that for system of locally interacting diffusions carrying discrete masses, subject to an environmental noise undergoing mass coagulation, its empirical measures corresponding different masses converge Stochastic Partial Differential Equations (SPDEs) with enha...

We prove the existence and Besov regularity of density solution to a general parabolic SPDE which includes stochastic Burgers equation on an unbounded domain. use elementary approach based fractional integration by parts.

We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise. We show that in some cases, in particular when the forcing is given by space-time white noise, it may happen that the homogenised SPDE is not what one would expect from existing results for PDEs with mor...

Diffusion processes intended to model the continuous state space limit of birth–death processes, chemical reactions, and other discrete particle systems often involve multiplicative noise where the diffusion vanishes near one (or more) of the state space boundaries. Standard direct numerical simulation schemes for the associated stochastic differential equations run the risk of “overshooting”, ...

In many applications it is important to be able to sample paths of SDEs conditional on observations of various kinds. This paper studies SPDEs which solve such sampling problems. The SPDE may be viewed as an infinite dimensional analogue of the Langevin SDE used in finite dimensional sampling. In this paper nonlinear SDEs, leading to nonlinear SPDEs for the sampling, are studied. In addition, a...