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Asymptotics of Intersection Local Time for Diffusion Processes

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Abstract

In the paper, we investigate the intersection local time for two correlated Brownian motions on the plane that form a diffusion process in ℝ4 associated with a divergence-form generator. Using Gaussian heat kernel bounds, we prove the existence of intersection local time for these Brownian motions, obtain estimates of its moments, and establish the law of iterated logarithm for it.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshenkivska str. 3, Kiev, 401601, Ukraine

    Andrey Dorogovtsev & Olga Izyumtseva

  2. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Peremohy ave. 37, Kiev, 03056, Ukraine

    Andrey Dorogovtsev

Authors
  1. Andrey Dorogovtsev
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  2. Olga Izyumtseva
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Correspondence to Andrey Dorogovtsev.

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Dedicated to Professor Vygantas Paulauskas on the occasion of his 75th birthday

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Dorogovtsev, A., Izyumtseva, O. Asymptotics of Intersection Local Time for Diffusion Processes. Lith Math J 59, 519–534 (2019). https://doi.org/10.1007/s10986-019-09466-5

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  • DOI: https://doi.org/10.1007/s10986-019-09466-5

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