I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “On a limit theorem related to probabilistic representation of the Cauchy problem solution for the Schrödinger equation”, Zap. Nauchn. Sem. POMI, 2016, Volume 454,Pages <nobr>158

This article is cited in 18 papers

On a limit theorem related to probabilistic representation of the Cauchy problem solution for the Schrödinger equation

I. A. Ibragimov^ab, N. V. Smorodina^ab, M. M. Faddeev^b

^a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
^b St. Petersburg State University, St. Petersburg, Russia

Abstract: We suggest a new method of a probabilistic approximation of the Cauchy problem solution for the unperturbed Schrödinger equation by expectations of functionals of some random walk. In contrast to our previous papers we do not suppose the existence of exponential moment for each step of the random walk.

Key words and phrases: limit theorem, random walk, Schrödinger equation, Feynman measure.

UDC: 519.2

Received: 17.10.2016