Perturbed Semigroup Limit Theorems with Applications to Discontinuous Random Evolutions
Perturbed Semigroup Limit Theorems with Applications to Discontinuous Random Evolutions
For $\varepsilon > 0$ small, let ${U^\varepsilon }(t)$ and $S(t)$ be strongly continuous semigroups of linear contractions on a Banach space $L$ with infinitesimal operators $A(\varepsilon )$ and $B$ respectively, where $A(\varepsilon ) = {A^{(1)}} + {\varepsilon A^{(2)}} + o()$ as $\varepsilon \to 0$. Let $\{ B(u);u \geqslant 0\}$ be …