On semigroups corresponding to storage processes. II (Q2730980)

[For part I see ibid. 11, 87-101 (1998; Zbl 0927.60075).]NEWLINENEWLINENEWLINEThe paper considers semigroups corresponding to stochastic processes \(X(t)\) governed by the equation \(X(t)= x- \int^t_0 r(X(s)) ds+ A(t)\), where \(r(x)\) is a nonnegative function on \([0,\infty)\) such that \(r(0)= 0\), \(r(x)> 0\) \((x> 0)\), left continuous and has positive right limits, and \(A(t)\) is an increasing Lévy process with \(Ee^{-\theta A(t)}= \exp\int^\infty_0 t(e^{-\theta y}- 1) v(dy)\). It is shown that this semigroup is strongly continuous on \(C([0, \infty])\). The domain of the generator is described when the total mass of the Lévy measure is finite. A core for the generator is given when \(r(x)\) is nondecreasing. Processes starting at infinity are also investigated.