I have a following stochastic model describing evolution of a process ($Y$) in space and time. Ds and Dt are domain in space (2D with $x$ and $y$ axes) and time (1D with $t$ axis). This model is usually known as mixed-effects model or components-of-variation models
I am currently developing Y as follow:
%# Time parameters T=1:1:20; % input nT=numel(T); %# Grid and model parameters nRow=100; nCol=100; [Grid.Nx,Grid.Ny,Grid.Nt] = meshgrid(1:1:nCol,1:1:nRow,T); xPower=0.1; tPower=1; noisePower=1; detConstant=1; deterministic_mu = detConstant.*(((Grid.Nt).^tPower)./((Grid.Nx).^xPower)); beta_s = randn(nRow,nCol); % mean-zero random effect representing location specific variability common to all times gammaTemp = randn(nT,1); for t = 1:nT gamma_t(:,:,t) = repmat(gammaTemp(t),nRow,nCol); % mean-zero random effect representing time specific variability common to all locations end var=0.1;% noise has variance = 0.1 for t=1:nT kappa_st(:,:,t) = sqrt(var)*randn(nRow,nCol); end for t=1:nT Y(:,:,t) = deterministic_mu(:,:,t) + beta_s + gamma_t(:,:,t) + kappa_st(:,:,t); end
Can someone help explain, through some illustration using Matlab, if I am correctly producing $Y$? Also, how to produce delta in the expression for $Y$?