Probabilistic technique of multiple integrals transformation into integrals of lower dimension

About the authors:

Vyacheslav E. Mosyagin, Cand. Sci. (Phys.-Math.), Associate Professor, Department of Mathematical Analysis and Function’s Theory, Institute of Mathematics and Computer Sciences, Tyumen State University
Natalya A. Shvemler, Post-graduate student, Department of Mathematical Analysis and Functions Theory, Institute of Mathematics and Computer Sciences, Tyumen State University

Abstract:

The article describes the dimensionality reduction technique of multiple integrals. The basic idea is that the representation a multiple integral as the expectation (Lebesgue integral) with respect to a suitable absolutely continuous probability distribution is possible. This representation allows us to use the probability concept of independence random variables in the integration theory. It also allows to apply the change-of-variables theorem in the Lebesgue integral that transforms an abstract integral to the integral over the real line.

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