Some aspects of strong inversion formulas of an SFT

  • Shigeyoshi OgawaEmail author
  • Hideaki Uemura
Original Paper Area 4


We study the question of invertibility of the stochastic Fourier transformation of a random function \(f(t,\omega )\). By the inversion of the SFT (short for “stochastic Fourier transformation”) we understand the two different meanings as follows; the reconstruction of the random function \(f(t,\omega )\) itself by only the SFT or the reconstruction of the \(f(t,\omega )\) with some supplemental information. The former we will call the inversion in strong sense and the latter the inversion in wide sense. The question of inversion in wide sense having been studied extensively in the previous papers, now in this note we are to study the question of invertibility in strong sense and show some typical results.


Stochastic Fourier transformation Inversion in strong sense Stochastic Fourier coefficient Itô integral Ogawa integral 

Mathematics Subject Classification

60H05 60H15 60H30 



We authors would like to express our sincere thanks to the reviewer for his/her valuable comments.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical ScienceRitsumeikan UniversityKusatsuJapan
  2. 2.Department of Mathematics EducationAichi University of EducationKariyaJapan

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