相关论文: Stable L\'{e}vy diffusion and related model fittin…

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…

In this paper subgrid multiscale stabilized finite element method for Advection-Diffusion-Reaction (ADR) equation coupled with Stokes-Darcy flow problem has been studied. Here the advection velocity involved in ADR equation obeys…

We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The…

The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…

We consider a process given as the solution of a one-dimensional stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. H\"older continuity of the Lebesgue density of…

Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Levy processes and have wide applications in engineering and physical sciences. The probability density of…

In this paper we consider an ESFEM method for the advection and diffusion of a scalar quantity on a moving closed curve. The diffusion process is controlled by a forcing term that may include a rough term (specifically a stochastic noise)…

We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that…

In Rajeev (2013), 'Translation invariant diffusion in the space of tempered distributions', it was shown that there is an one to one correspondence between solutions of a class of finite dimensional SDEs and solutions of a class of SPDEs in…

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the…

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

By use of Lagrangian tracers propagated on 2D simulations of Scrape-Off Layer (SOL) turbulence, we are able to determine the non-local fractional-advection, fractional-diffusion equation (FADE) coefficients for a number of equilibrium…

We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…

Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their…

The asymptotic behavior of a class of stochastic reaction-diffusion-advection equations in the plane is studied. We show that as the divergence-free advection term becomes larger and larger, the solutions of such equations converge to the…

A new, improved split-step backward Euler (SSBE) method is introduced and analyzed for stochastic differential delay equations(SDDEs) with generic variable delay. The method is proved to be convergent in mean-square sense under conditions…

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…

In this paper we investigate the regularity properties of strong solutions to SDEs driven by L\'evy processes with irregular drift coefficients. Under some mild conditions, we show that the singular SDE has a unique strong solution for each…

Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…

We consider stochastic differential equations (SDEs) driven by Feller processes which are themselves solutions of multivariate Levy driven SDEs. The solutions of these 'iterated SDEs' are shown to be non-Markovian. However, the process…