Let {XN(t), t0}, N = 1,2,be a sequence of continuous-parameter Markov processes, and let T,(t)f(x)= EX[f(X,(t))]. Suppose that lim,NcT^(t)f(x)= T(t)f(x), and that convergence is uniform over x and over t E [0, K] for all K < o. When is convergence uniform over t E [0, oo)? Questions of this type are considered under the auxiliary condition that T(t)f(x) converges uniformly over x as t -> oo. A ...

Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the...

Abstract. We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W -functional of the limiting process. The class of the W -functionals, that can be obtained as the limiting ones, is completely described in the terms of the associated W -...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

We study the effect of approximation matrices to semi-discrete relaxation schemes for the equations of one-dimensional elastodynamics. We consider a semi-discrete relaxation scheme and establish convergence using the Lp theory of compensated compactness. Then we study the convergence of an associated relaxation-diffusion system, inspired by the scheme. Numerical comparisons of fully-discrete sc...

rice is one of the most widely human consumed agricultural products. for a prevention or diminishing of rice cracking in its milling process, precision control of drying conditions is indispensable. in this research, a thin layer experimental dryer is employed to obtain paddy’s drying kinetics. drying experiments were conducted at five inlet temperatures of drying air of 30, 40, 50, 60 and 70 °...

Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxilia...