This article is cited in 10 papers

Symmetric integrals and stochastic analysis

F. S. Nasyrov

Ufa State Aviation Technical University

Abstract: Symmetric integrals of the Stieltjes type for an arbitrary continuous function and which are determinate versions of the Stratonovich stochastic integrals are defined. It is shown that the solution of a pathwise analogue of stochastic differential equations with a symmetric integral and Itô stochastic differential equations is reduced to a solution of a system of ordinary differential equations. The relation between improper symmetric integrals, which is extended to symmetric integrals and Hellinger integrals, is established.

Keywords: symmetric integral, Stratonovich stochastic integral, stochastic differential equation, improper symmetric integral, Hellinger integral.

Received: 23.04.2003

DOI: 10.4213/tvp36

 English version: Theory of Probability and its Applications, 2007, 51:3, 486–503

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