

Principle Seminar of the Department of Probability Theory, Moscow State University
March 23, 2016 16:45–17:45, Moscow, MSU, auditorium 1224






Asymptotic properties of selfintersection local times of Gaussian integrators
A. A. Dorogovtsev^{}, O. Izyumtseva^{} ^{} Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev

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Abstract:
Integrators are the class of Gaussian processes which allows the denition
of stochastic integral with respect to any process from that class for any non
random square integrable integrand. Integrators can be obtained by the second
quantization of the Wiener process. Since that all properties of integrator are
completely dened by the properties of continuous linear operator in the space
of square integrable functions which generate the second quantization. Planar
integrators can serve for construction of Polymer models. This fact increases
the interest to the questions of existence and properties of local time and self
intersection local times for integrators (see papers of authors). The main result
of the talk is the large deviations for the selfintersection local time of integrators
in terms of generating them operators. The main tools of the proof are Gaussian
estimates, the large deviations technique and statements from the geometry of
Hilbert space.
References

Dorogovtsev, A. A.; Izyumtseva, O. L. Local selfintersection times for Gaussian processes in the plane. (Russian) Dokl. Akad. Nauk 454 (2014), no. 3, 262264; translation in Dokl. Math. 89 (2014), no. 1, 5456.

Dorogovtsev, Andrey A.; Izyumtseva, Olga L. Asymptotic and geometric properties of compactly perturbed Wiener process and selfintersection local time. Commun. Stoch. Anal. 7 (2013), no. 2, 337–348.

Andrey Dorogovtsev, Olga Izyumtseva .Properties of Gaussian local times . Lithuanian Math. Journal, v. 55, no. 4, 2015, p. 489 — 505.

