Asymptotic properties of self-intersection local times of Gaussian integrators

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 self-intersection 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

1. Dorogovtsev, A. A.; Izyumtseva, O. L. Local self-intersection 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.
2. Dorogovtsev, Andrey A.; Izyumtseva, Olga L. Asymptotic and geometric properties of compactly perturbed Wiener process and self-intersection local time. Commun. Stoch. Anal. 7 (2013), no. 2, 337–348.
3. Andrey Dorogovtsev, Olga Izyumtseva .Properties of Gaussian local times . Lithuanian Math. Journal, v. 55, no. 4, 2015, p. 489 — 505.