A two-dimensional linear birth and death process is a continuous-time Markov chain Y(·) with state space (Z+)2 which can jump from the point (n, m) to one of its four neighbors, with rates that are linear functions of n and m. Criteria are extended for determining whether such a process has a positive probability or zero probability of escaping to infinity. In the transient case considered, the projections of the imbedded Markov chain {Xn} of the successive states visited by Y(·) on a suitable pair of orthonormal vectors v and w are shown to be regularly varying sequences with index 1. Specifically, (Xn, v)∽δn and (Xn, w)∽ kn/log n for positive constants δ and k.
We set out the main features of Maple V, Release 3, and discuss its potential value to econometricians. Computer algebra systems, of which Maple is a leading example, have developed with the increased power of modern computers, but require skill and patience to use. It seems likely they will find a place in the econometrician's toolkit for work at the interface between analytic and numerical work, where they should prove valuable. However, although Maple has many of the features of conventional statistical/econometric/numerical software, it should not be seen as a substitute.
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