相关论文: A Singular Parabolic Anderson Model

We estimate nonparametrically the spatially varying diffusivity of a stochastic heat equation from observations perturbed by additional noise. To that end, we employ a two-step localization procedure, more precisely, we combine local state…

We consider nonlinear parabolic SPDEs of the form $\partial_t u=-(-\Delta)^{\alpha/2} u + b(u) +\sigma(u)\dot w$, where$\dot w$ denotes space-time white noise. The functions $b$ and $\sigma$ are both locally Lipschitz continuous. Under some…

This paper aims to investigate the asymptotic error distribution of several numerical methods for stochastic partial differential equations (SPDEs) with multiplicative noise. Firstly, we give the limit distribution of the normalized error…

We have developed a semi-analytical framework formulated in the canonical fermion representation to investigate strongly correlated electron systems. We consider the U=$\infty$ Hubbard model and used the equation of motion method to…

We study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous datum, of the form $$ \begin{cases} \displaystyle u_t -…

This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…

The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem…

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in…

Consider the stochastic heat equation $\partial_t u = (\frac{\varkappa}{2})\Delta u+\sigma(u)\dot{F}$, where the solution $u:=u_t(x)$ is indexed by $(t,x)\in (0, \infty)\times\R^d$, and $\dot{F}$ is a centered Gaussian noise that is white…

The recently developed energy-scale-dependent Composite Operator Method is applied to the single-impurity Anderson model. A fully self-consistent solution is given and analyzed. At very low temperatures, the density of states presents, on…

In this paper we prove existence and uniqueness results for nonlinear parabolic problems with Dirichlet boundary values whose model is \[ \left\{ \begin{aligned} &b(u)_t-\Delta_{p}u=\mu\;\mbox{in }(0,T)\times\Omega,\\…

Density of states, dynamic (optical) conductivity and phase diagram of paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean-field theory (DMFT+Sigma…

Consider non-linear time-fractional stochastic heat type equations of the following type, $$\partial^\beta_tu_t(x)=-\nu(-\Delta)^{\alpha/2} u_t(x)+I^{1-\beta}_t[\lambda \sigma(u)\stackrel{\cdot}{F}(t,x)]$$ in $(d+1)$ dimensions, where…

The parabolic Anderson problem is the Cauchy problem for the heat equation with random potential and localized initial condition. In this paper we consider potentials which are constant in time and independent exponentially distributed in…

The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three…

We study the temperature dependence of the specific heat in the periodic Anderson model as function of the on-site Coulomb interaction, hybridization, and position of the f-electrons energy level. At strong coupling (U=infinity) we use…

We study the parabolic Anderson model (PAM) \begin{equation} {\partial \over \partial t}u(t,x) =\frac{1}{2}\Delta u(t,x) + u(t,x)\xi(x), \quad t>0, x\in \mathbb{R}^d, \quad \text{and} \quad u(0,x) \equiv 1, \quad \forall x\in \mathbb{R}^d,…

In this paper, we consider an inference problem for the first order autoregressive process with non-zero mean driven by a long memory stationary Gaussian process. Suppose that the covariance function of the noise can be expressed as…

This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $\nu$ whose components have paths of bounded variation. The presence of the process $\nu$ prevents from…

We consider the stochastic heat equation with multiplicative noise $u_t={1/2}\Delta u+ u \diamond \dot{W}$ in $\bR_{+} \times \bR^d$, where $\diamond$ denotes the Wick product, and the solution is interpreted in the mild sense. The noise…