Some Integration-by-Parts Formulas Involving 2-Copulas

X. Li, P. Mikusiński and M. D. Taylor
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X. Li: University of Central Florida
P. Mikusiński: University of Central Florida
M. D. Taylor: University of Central Florida

A chapter in Distributions With Given Marginals and Statistical Modelling, 2002, pp 153-159 from Springer

Abstract: Abstract Abstract We note examples of probabilistic interpretations of integrals involving 2-copulas. We then use the theory of strong convergence of copulas to justify an integration-by-parts formula involving 2-copulas, % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qeaeaaca % WGMbWaaeWaaeaacaWGbbaacaGLOaGaayzkaaGaamizaiaadkeacqGH % 9aqpdaWdXaqaaiaadAgadaqadaqaaiaadshaaiaawIcacaGLPaaaca % WGKbGaamiDaiabgkHiTmaapebabaGabmOzayaafaWaaeWaaeaacaWG % bbaacaGLOaGaayzkaaGaamiramaaBaaaleaacaaIXaaabeaakiaadg % eacaaMc8UaamiramaaBaaaleaacaaIYaaabeaakiaadkeacqGH9aqp % daWdXaqaaiaadAgadaqadaqaaiaadshaaiaawIcacaGLPaaacaWGKb % GaamiDaiabgkHiTmaapebabaGabmOzayaafaWaaeWaaeaacaWGbbaa % caGLOaGaayzkaaGaamiramaaBaaaleaacaaIYaaabeaakiaadgeaca % aMc8UaamiramaaBaaaleaacaaIXaaabeaakiaadkeacaGGUaaaleaa % caWGjbWaaWbaaWqabeaacaaIYaaaaaWcbeqdcqGHRiI8aaWcbaGaaG % imaaqaaiaaigdaa0Gaey4kIipaaSqaaiaadMeadaahaaadbeqaaiaa % ikdaaaaaleqaniabgUIiYdaaleaacaaIWaaabaGaaGymaaqdcqGHRi % I8aaWcbaGaamysamaaCaaameqabaGaaGOmaaaaaSqab0Gaey4kIipa % aaa!705B! $$ \int_{{I^2}} {f\left( A \right)dB = \int_0^1 {f\left( t \right)dt - \int_{{I^2}} {f'\left( A \right){D_1}A\,{D_2}B = \int_0^1 {f\left( t \right)dt - \int_{{I^2}} {f'\left( A \right){D_2}A\,{D_1}B.} } } } } $$ where A and B are arbitrary 2-copulas and f is continuously differentiable.

Keywords: Integration-by-parts; Strong convergence; Identity (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-017-0061-0_16

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