On coupling of stochastic processes with embedded point processes (Q1323518)

The subject of this paper is the coupling of pairs \((Z, S)\), where \(Z\) is a stochastic process and \(S\) is an embedded point process whose points may be thought of as regeneration points. After giving the definitions of ``traditional'', wide sense, semi- and weak regeneration, the authors give criteria for these, involving two random variables \(0\leq S_ 0< S_ 1<\infty\) such that the \(\text{post-}S_ 0\) \(Z\)-process has the same distribution as the \(\text{post-} S_ 1\) \(Z\)-process. They also give sufficient conditions for the successful coupling of two processes \(Z^ 1\), \(Z^ 2\) with embedded point processes \(S^ 1\), \(S^ 2\), in terms of two random sequences \((W^ 1_ n)_ 0\), \((W^ 2_ n)_ 0\) such that \((S^ 1, W^ 1)\) and \((S^ 2, W^ 2)\) can be successfully coupled.