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- W1966284818 abstract "If <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-brace mu Subscript n Baseline right-brace> <mml:semantics> <mml:mrow> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{ {mu _n}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-brace nu Subscript n Baseline right-brace> <mml:semantics> <mml:mrow> <mml:mo>{</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>ν<!-- ν --></mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:mo>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>left { {{nu _n}} right }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are two sequences of probability measures on a separable metric space, we give conditions under which <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-brace mu Subscript n Baseline right-brace> <mml:semantics> <mml:mrow> <mml:mo>{</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:mo>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>left { {{mu _n}} right }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> satisfies a large deviation principle if and only if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-brace nu Subscript n Baseline right-brace> <mml:semantics> <mml:mrow> <mml:mo>{</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>ν<!-- ν --></mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:mo>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>left { {{nu _n}} right }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> does. A known and a new theorem follow immediately from the application of this comparison principle to standard results in large deviation theory." @default.
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- W1966284818 date "1988-01-01" @default.
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- W1966284818 title "A comparison principle for large deviations" @default.
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