I am dealing with a multivariate Ornstein Uhlenbeck style SDE. Specifically $dx_{t,j}=\kappa_{j}(x_{t,j-1}-x_{t,j})dt+\sigma dW_{t,j} $ here j=1,2,...,6 , $x_{t,0}=\theta$ , $\kappa_{1}<\kappa_{2}<...<\kappa_{6}$ and $W_{j}$ are independent.
I need to restrict $x_{t,j}$'s to have decreasing concave or increasing convex shape at each time t. I couldn't figure out how I should change my SDE to have this kind of restriction. Or even if it is possible? Thank you for any help.