Related papers: Heat kernel regularization of the effective action…
In previous work [cond-mat/9904207,cond-mat/9904215] we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential…
We present a new method to renormalize stochastic differential equations subjected to multiplicative noise. The method is based on the widely used concept of effective potential in high energy physics, and has already been successfully…
We consider a semilinear stochastic heat equation in spatial dimension at least $3$, forced by a noise that is white in time with a covariance kernel that decays like $\lvert x\rvert^{-2}$ as $\lvert x\rvert\to\infty$. We show that in an…
The stationary state of stochastic processes such as reaction-diffusion systems can be related to the ground state of a suitably defined quantum Hamiltonian. Using this analogy, we investigate the applicability of a real space…
We develop a heat kernel method to compute the one-loop effective action for a general class of nonlinear electrodynamic (NLED) theories in four dimensional Minkowski spacetime. Working in the background field formalism, we extract the…
We study stochastic reaction--diffusion equation $$ \partial_tu_t(x)=\frac12 \partial^2_{xx}u_t(x)+b(u_t(x))+\dot{W}_{t}(x), \quad t>0,\, x\in D $$ where $b$ is a generalized function in the Besov space…
We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter…
In this article we present a {\it quantitative} central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space-time white noise and the white-colored noise…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
In view of some recent results in case of the dopaminergic neurons exhibiting long range correlations in VTA of the limbic brain we are interested to find out whether any stochastic nonlinear response may be reproducible in the nano scales…
By working with the periodic resolvent kernel and Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction diffusion…
Recently, the problem of boundary stabilization and estimation for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However,…
We consider the stochastic reaction-diffusion equation in $1+1$ dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-H\"older space with any regularity index larger than $-1$. We…
We consider the stochastic heat equation on $\mathbb R^d$ with multiplicative space-time white noise noise smoothed in space. For $d\geq 3$ and small noise intensity, the solution is known to converge to a strictly positive random variable…
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…
We approximate the white-noise driven stochastic heat equation by replacing the fractional Laplacian by the generator of a discrete time random walk on the one dimensional lattice, and approximating white noise by a collection of i.i.d.…
A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method…
We study the large-scale behaviour of a family of stochastic reaction-diffusion equations driven by long-range correlated noise in a weakly nonlinear regime. Depending on the decay of correlations of the noise and the strength of the…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
On metric measure spaces with sub-Gaussian heat kernel behavior in small time, we obtain a sufficient condition to solve Wick renormalized stochastic quantization equations with polynomial interaction. Given the power of the nonlinearity,…