Strong renewal theorems with infinite mean
Strong renewal theorems with infinite mean
Let <italic>F</italic> be a nonarithmetic probability distribution on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 0 comma normal infinity right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(0,\infty )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and suppose <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1 minus upper F left-parenthesis t right-parenthesis"> …