Generalized jump-type Ornstein-Uhlenbeck processes as limits of infinite- particle systems (Q1262609)

The author proves the existence and uniqueness in law, via martingale problems, of linear jump-type processes of the form \[ X(t)(\phi)=X(0)(\phi)+\int^{t}_{0}X(s)(A\phi)ds+Z(t)(\phi),\quad t\geq 0, \] for all \(\phi\in {\mathcal S}({\mathbb{R}}^ d)\), where A is a suitable nonnegative-definite operator from \({\mathcal S}({\mathbb{R}}^ d)\) into itself and \(\{\) Z(t), \(t\geq 0\}\) is an \({\mathcal S}'({\mathbb{R}}^ d)\)-valued independent increment process. This extends a result of \textit{R. A. Holley} and \textit{D. W. Stroock} [Publ. Res. Inst. Math. Sci. 14, 741-788 (1978; Zbl 0412.60065)] who considered the case of continuous paths.