Geodesic
Symmetric integrals and stochastic analysis
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 496-517

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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. 
F. S. Nasyrov. Symmetric integrals and stochastic analysis. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 496-517. http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a3/
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