Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CONDITIONAL INTEGRAL TRANSFORMS AND CONVOLUTIONS FOR A GENERAL VECTOR-VALUED CONDITIONING FUNCTIONS

  • Kim, Bong Jin (Department of Mathematics Daejin University) ;
  • Kim, Byoung Soo (School of Liberal Arts Seoul National University of Science and Technology)
  • Received : 2016.07.30
  • Accepted : 2016.09.11
  • Published : 2016.09.30
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Abstract

We study the conditional integral transforms and conditional convolutions of functionals defined on K[0, T]. We consider a general vector-valued conditioning functions $X_k(x)=({\gamma}_1(x),{\ldots},{\gamma}_k(x))$ where ${\gamma}_j(x)$ are Gaussian random variables on the Wiener space which need not depend upon the values of x at only finitely many points in (0, T]. We then obtain several relationships and formulas for the conditioning functions that exist among conditional integral transform, conditional convolution and first variation of functionals in $E_{\sigma}$.

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References

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