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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 1, Pages 43–61 (Mi tvp300)  

This article is cited in 3 scientific papers (total in 3 papers)

Random mappings and a generalized additive functionals of a Wiener process

A. A. Dorogovtsev, V. V. Bakunin

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: The definition of a generalized additive homogeneous functional of a Wiener process is introduced. It is shown that a generalized functional is uniquely specified by its characteristics. In this case the functions from the Schwartz space $S^*$ of slowly growing generalized functions play the role of generating functions.

Keywords: generalized Wiener functionals, multiple stochastic integrals, additive functionals.

DOI: https://doi.org/10.4213/tvp300

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English version:
Theory of Probability and its Applications, 2004, 48:1, 63–79

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Received: 20.04.2000

Citation: A. A. Dorogovtsev, V. V. Bakunin, “Random mappings and a generalized additive functionals of a Wiener process”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 43–61; Theory Probab. Appl., 48:1 (2004), 63–79

Citation in format AMSBIB
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\paper Random mappings and a generalized additive functionals of a Wiener process
\jour Teor. Veroyatnost. i Primenen.
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\vol 48
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\pages 43--61
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\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
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\pages 63--79
\crossref{https://doi.org/10.1137/S0040585X980269}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Uemura H., “Generalized positive continuous additive functionals of multidimensional Brownian motion and their associated Revuz measures”, Stochastic Processes and Their Applications, 118:10 (2008), 1870–1891  crossref  mathscinet  zmath  isi  scopus
    2. A. A. Dorogovtsev, O. L. Izyumtseva, “On regularization of the formal Fourier–Wiener transform of the self-intersection local time of a planar Gaussian process”, Theory Stoch. Process., 17(33):1 (2011), 28–38  mathnet  mathscinet  zmath
    3. Dorogovtsev A.A., Izyumtseva O.L., “Local Times of Self-Intersection”, Ukr. Math. J., 68:3 (2016), 325–379  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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