We start from a basic model for the transport of charged species in heterostructures containing the mechanisms diffusion, drift and reactions in the domain and at its boundary. Considering limit cases of partly fast kinetics we derive reduced models. This reduction can be interpreted as some kind of projection scheme for the weak formulation of the basic electro–reaction–diffusion system. We ve...

Linear-implicit versions of strong Taylor numerical schemes for finite dimensional It6 stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an 7 strong linear-implicit Taylor scheme with time-step A applied to the N dimensional It6-Galerkin SDE for a class of parabolic stochastic partial diff...

1 We present efficient partial differential equation (PDE) methods for continuous time mean2 variance portfolio allocation problems when the underlying risky asset follows a stochastic 3 volatility process. The standard formulation for mean variance optimal portfolio allocation 4 problems gives rise to a two-dimensional non-linear Hamilton-Jacobi-Bellman (HJB) PDE. We 5 use a wide stencil metho...

Semi-active base isolation system has been proposed mainly to mitigate the base drift of isolated structures while in most cases, its application causes the maximum acceleration of superstructure to be increased. In this paper, designing optimal semi-active base isolation system composed of linear base isolation system with low damping and magneto-rheological (MR) damper has been studied for co...

We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class includes many interesting processes in real applications, e.g., Ornstein-Uhlenbeck, growth processes and geometric Brownian motion with time dependent drift. This m...

We study the asymptotic behavior of the Maximum Likelihood and Least Squares Estimators of a k-monotone density g0 at a fixed point x0 when k > 2. We find that the j th derivative of the estimators at x0 converges at the rate n−(k−j)/(2k+1) for j = 0, . . . , k − 1. The limiting distribution depends on an almost surely uniquely defined stochastic process Hk that stays above (below) the k-fold i...

We consider finite-range asymmetric exclusion processes on Z with non-zero drift. The diffusivity D(t) is expected to be of O(t). We prove that D(t) ≥ Ct in the weak (Tauberian) sense that ∫∞ 0 e tD(t)dt ≥ Cλ as λ → 0. The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process, for which the result is a consequence of the scaling limi...

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian motion. Its role is comparable to the role of the...

We consider finite-range asymmetric exclusion processes on Z with non-zero drift. The diffusivity D(t) is expected to be of O(t1/3). We prove that D(t) ≥ Ct1/3 in the weak (Tauberian) sense that ∫∞ 0 e −λttD(t)dt ≥ Cλ−7/3 as λ → 0. The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process, for which the result is a consequence of the...

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process \the invelope" and show that it is an almost surely uniquely de ned function of integrated Brownian motion. Its role is comparable to the role of the ...