Gaussian measure of large balls in a Hilbert space
Gaussian measure of large balls in a Hilbert space
Let <bold>P</bold> be a zero mean Gaussian measure in a Hilbert space. The asymptotic behavior of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P left-brace double-vertical-bar x minus b double-vertical-bar squared greater-than epsilon right-brace"> <mml:semantics> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow> <mml:mo symmetric="true">‖</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>x</mml:mi> <mml:mo>−</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> …