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On a transformation of the wiener process in ℝm by a functional of the local time type on a surface

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Abstract

A transformation of the Wiener process ξt in ℝm is considered. This transformation is realized by a multiplicative functional αl=u(ξl/u(ξ0), where the functionu is constructed in a certain way by using a functional of the local time type on a surface. It is proved that this transformation is equivalent to the successive application of an absolutely continuous change of a measure and killing on the surface.

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References

  1. V. S. Vladimirov,Equations in Mathematical Physics [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  2. N. I. Portenko,Results in the Theory of Additive Functional of Markov Processes [in Russian], Author's Abstract of the Candidate Degree Thesis (Physics and Mathematics), Kiev (1967).

  3. E. B. Dynkin,Markov Processes [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  4. N. I. Portenko,Generalized Diffusion Processes [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

  5. P. Sh. Liptser and A. N. Shiryaev,Statistics of Random Processes [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  6. N. I. Portenko, “On the theory of diffusion processes,” in:Probability and Mathematical Statistics. Proceedings of the 6th USSR Japan Symposium, World Scientific, Singapore (1992), pp. 259–267.

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Authors and Affiliations

  1. Kiev University, Kiev

    M. M. Osipchuk

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  1. M. M. Osipchuk
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 863–866, June, 1993.

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Osipchuk, M.M. On a transformation of the wiener process in ℝm by a functional of the local time type on a surface. Ukr Math J 45, 954–958 (1993). https://doi.org/10.1007/BF01061446

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  • DOI: https://doi.org/10.1007/BF01061446

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