Self-intersection local time for compactly perturbed Wiener processes

Olga Izyumtseva, Institute of Mathematics of the National Academy of Sciences of Ukraine. Part of the Probability, Stochastic Modelling and Financial Mathematics seminar.

Speaker: Olga Izyumtseva

Title: Self-intersection local time for compactly perturbed Wiener processes

Abstract: In the talk we consider Gaussian processes whose families of increments on the small time intervals have similar behavior to the behavior of increments of Wiener process. Such processes are constructed by the perturbation with compact operators in white noise space. Obtained processes are special case of Gaussian integrators. The law of iterated logarithm and asymptotic of small ball probabilities can be established for it.  But the main advantage of the introduced processes is the possibility to build Rosen renormalization for the self-intersection local times in the planar case. We present corresponding statement in terms of Fourier-Wiener transform. The talk is based on the joint works with Andrey Dorogovtsev.

 

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