Abstract
We investigate properties of local time for one class of Gaussian processes. These processes are called integrators since every function from L 2([0; 1]) can be integrated over it. Using the white noise representation, we can associate integrators with continuous linear operators in L 2([0; 1]). In terms of these operators, we discuss the existence and properties of local time for integrators. Also, we study the asymptotic behavior of Brownian self-intersection local time as its end-point tends to infinity.
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*The work was partially supported by the Presidium of National Academy of Sciences of Ukraine as a part of the joint scientific project with the Russian foundation of fundamental research, project number 09-01-14.
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Dorogovtsev, A., Izyumtseva, O. Properties of Gaussian local times. Lith Math J 55, 489–505 (2015). https://doi.org/10.1007/s10986-015-9294-8
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DOI: https://doi.org/10.1007/s10986-015-9294-8