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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 3, Pages 496–517
DOI: https://doi.org/10.4213/tvp36 (Mi tvp36) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Symmetric integrals and stochastic analysis

F. S. Nasyrov

Ufa State Aviation Technical University
Full-text PDF (1815 kB) Citations (9)
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DOI: https://doi.org/10.4213/tvp36
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
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 3, Pages 486–503
DOI: https://doi.org/10.1137/S0040585X97982499
Bibliographic databases:
Language: Russian
Citation: F. S. Nasyrov, “Symmetric integrals and stochastic analysis”, Teor. Veroyatnost. i Primenen., 51:3 (2006), 496–517; Theory Probab. Appl., 51:3 (2007), 486–503
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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