Related papers: Effective Approximation for a Stochastic System wi…
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
This paper considers a family of second-order periodic parabolic equations with highly oscillating potentials, which have been considered many times for the time-varying potentials in stochastic homogenization. Following a standard…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
For a class of finite elements approximations for linear stochastic parabolic PDEs it is proved that one can accelerate the rate of convergence by Richardson extrapolation. More precisely, by taking appropriate mixtures of finite elements…
We study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) which include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation. We propose a fully…
Explicit conditions are presented for the existence, uniqueness and ergodicity of the strong solution to a class of generalized stochastic porous media equations. Our estimate of the convergence rate is sharp according to the known optimal…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on a bounded spatial domain.…
We give a factorization procedure for a strictly hyperbolic partial differential operator of second order with logarithmic slow scale coefficients. From this we can microlocally diagonalize the full wave operator which results in a coupled…
This work is concerned with the identification problem for what we call the perturbation term or error term in a parabolic partial differential equation, through its approximate periodic solutions. The observation is made over a subregion…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a…
We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such…
In this paper, we establish the existence and uniqueness of solutions of elliptic-parabolic stochastic Keller-Segel systems. The solution is obtained through a carefully designed localization procedure together with some a priori estimates.…
The problem is analyzed of extrapolating power series, derived for an asymptotically small variable, to the region of finite values of this variable. The consideration is based on the self-similar approximation theory. A new method is…
We address the homogenization of a semilinear hyperbolic stochastic partial differential equation with highly oscillating coefficients, in the context of ergodic algebras with mean value. To achieve our goal, we use a suitable variant of…
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the…