In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the influence of the random domain perturbation on the solution. We derive deterministic partial differential equations to approximate the random solution’s mean and its covariance wit...

in the present study an alternative model allows the extension of the debye-hückel theory (dht) considering time dependence explicitly. from the electro-quasistatic approach (eqs) done in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles in arbitrary solutions acting as electrolytes.this...

We solve the open problem of characterizing the leading constant in the asymptotic approximation to the expected cost used for random partial match queries in random k-d trees. Our approaches are new and of some generality; in particular, they are applicable to many problems involving differential equations (or difference equations) with polynomial coefficients.

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

In this paper we develop an L2-theory for stochastic partial differential equations driven by Lévy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of the coefficients is assumed.