Specialization: 011200 Physics
Program: 07 Methods and problems of mathematical and computational physics
Department of higher mathematics and mathematical physics
Scientific adviser: prof. N.V. Smorodina
Reviewer: prof. Y.I. Belopol’skaya

Limit theorems on convergence to signed infinitely divisible measures and their applications
M.V. Platonova

In the first part of this paper we study properties of generalized infinitely divisible distributions with the Lévy measure which has a high singularity at zero. Such measures are signed ones and hence they are not probability measures. We show that in some sense these signed measures are limit measures for sums of independent random variables. In the last section using the positive part (the positive tail) of the limit measure we prove a theorem about large deviations of sums of independent random variables.
In the second part we construct a probabilistic approximation in the Sobolev’s spaces of the Cauchy problem solution for an evolution equation with the Riemann-Liouville’s operator of order over two on the right side. We use classical probabilistic methods and methods of the generalized function theory.

	The list of publications
	1.  Platonova M. V., Nonprobabilistic infinitely divisible distributions: the Lévy -Khinchin representation, limit theorems // Zap. Nauchn. Sem. POMI, 431(2014), 145-177, (in Russian).