Related papers: A stochastic approach to enhanced diffusion
This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a…
Stochastic processes of bridge types having pinned initial and terminal conditions have been widely used in applied research areas, but they all have a common drawback in that the model at hand is possibly misspecified owing to its…
In this paper, we consider a stochastic balance law with a Lipschitz flux and gain the uniqueness for stochastic entropy solutions. The argument is supported by the stochastic kinetic formulation, the It\^{o} formula and the regularization…
Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…
Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulas w.r.t. increments of the time are presented for…
We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for…
We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal…
We consider a simple model of the evolution of the concentration of a tracer, subject to a background shear flow by a fluid with viscosity $\nu \ll 1$ in an infinite channel. Taylor observed in the 1950's that, in such a setting, the tracer…
We solve the stationary Navier-Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosty in domains with unbounded outlets, in the case of shear thickening viscosity, i.e. the viscosity is given by the shear…
We discuss stochastic representations of advection diffusion equations with variable diffusivity, stochastic integrals of motion and generalized relative entropies.
This paper is concerned with the analysis of speed-up of reaction-diffusion-advection traveling fronts in infinite cylinders with periodic boundary conditions. The advection is a shear flow with a large amplitude and the reaction is…
We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…
We are interested in an anisotropic singular diffusion equation in the plane and in its regularization. We establish existence, uniqueness and basic regularity of solutions to both equations. We construct explicit solutions showing the…
We report accelerating diffusive solutions to the diffusion equation with a constant diffusion tensor. The maximum values of the diffusion density evolve in an accelerating fashion described by Airy functions. We show the diffusive…
We study the smoothness of the upper and lower value functions of stochastic differential games in the framework of time-homogeneous (possibly degenerate) diffusion processes in a domain, under the assumption that the diffusion, drift and…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
We present several results on the smoothness in $L_{p}$ sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form…
We study one-dimensional stochastic differential equations of form $dX_t = \sigma(X_t)dY_t$, where $Y$ is a suitable H\"older continuous driver such as the fractional Brownian motion $B^H$ with $H>\frac12$. The innovative aspect of the…
In stochastic analysis, the flow of information through time is typically modelled using a filtration. We introduce some of the basic ideas involving enlargements of filtration. Here, we focus mainly on initial enlargements, where a given…