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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TVP_2006_51_3_a3,
     author = {F. S. Nasyrov},
     title = {Symmetric integrals and stochastic analysis},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {496--517},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a3/}
}
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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/