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Perturbed semigroup limit theorems with applications to discontinuous random evolutions

Perturbed semigroup limit theorems with applications to discontinuous random evolutions

For <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="epsilon greater-than 0"> <mml:semantics> <mml:mrow> <mml:mi>ε<!-- ε --></mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\varepsilon &gt; 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> small, let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U Superscript epsilon Baseline left-parenthesis t right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>U</mml:mi> <mml:mi>ε<!-- ε --></mml:mi> </mml:msup> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> …