We consider in this paper a class of vector valued processes that have the form Yn+1 = An(Yn)+ Bn. Bn is assumed to be stationary ergodic and An is assumed to have a divisibility property. This class includes linear stochastic difference equations as well as multi-type branching processes (with a discrete or with a continuous state space). We derive explicit expressions for the probability dist...

Two new finite difference schemes based on the method of characteristics are presented for convection-diffusion problems. Both of the schemes are of second order in time, and the matrices of the derived systems of linear equations are symmetric. No numerical integration is required for them. The one is of first order in space and the other is of second order. For the former scheme, an optimal e...

In this paper, we investigate even-order linear difference equations and their criticality. However, restrict our attention only to several special cases of the general Sturm–Liouville equation. We wish on such a possible converse known theorem. This theorem holds for second-order as an equivalence; however, one implication is equations. First, show in sense term Later, upper bound criticality ...