This paper concerns the fluid dynamics modelled by the stochastic flow ï£± ï£² ï£³ Î·Ì‡ (t, x) = u (t,Î· (t, x)) + Ïƒ (t,Î· (t, x)) â—¦ áº† Î·(0, x) = x where the turbulent term is driven by the white noise áº† . Theâ€¦ (More)

driven by white noise áº† . Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navierâ€“Stokes equationâ€¦ (More)

The objective of this paper is to develop an approach to nonlinear ltering which allows the separation of time consuming computations involving the coe cients of the system from those dealing withâ€¦ (More)

The objective of this paper is to develop an approach to nonlinear filtering based on the Cameronâ€“Martin version of Wiener chaos expansion. This approach gives rise to a new numerical scheme forâ€¦ (More)

469 2013 Proc. R. Soc. A D. Venturi, X. Wan, R. Mikulevicius, B. L. Rozovskii and G. E. Karniadakis and simulations stochastic partial differential equations: analysis Malliavin approximation toâ€¦ (More)

A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as theâ€¦ (More)

We extend Krylovâ€™s Lp-solvability theory to the Cauchy problem for systems of parabolic stochastic partial differential equations (SPDEs). Some additional integrability and regularity properties areâ€¦ (More)