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Ukrainian Mathematical Journal

, Volume 52, Issue 9, pp 1403–1431 | Cite as

Nonlinear Transformations of Smooth Measures on Infinite-Dimensional Spaces

  • A. M. Kulik
  • A. Yu. Pilipenko
Article

Abstract

We investigate the properties of the image of a differentiable measure on an infinitely-dimensional Banach space under nonlinear transformations of the space. We prove a general result concerning the absolute continuity of this image with respect to the initial measure and obtain a formula for density similar to the Ramer–Kusuoka formula for the transformations of the Gaussian measure. We prove the absolute continuity of the image for classes of transformations that possess additional structural properties, namely, for adapted and monotone transformations, as well as for transformations generated by a differential flow. The latter are used for the realization of the method of characteristics for the solution of infinite-dimensional first-order partial differential equations and linear equations with an extended stochastic integral with respect to the given measure.

Keywords

Differential Equation Banach Space Partial Differential Equation Linear Equation Structural Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • A. M. Kulik
    • 1
  • A. Yu. Pilipenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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