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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 1, Pages 52–80
DOI: https://doi.org/10.4213/tvp158 (Mi tvp158) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Constructing a stochastic integral of a nonrandom function without orthogonality of the noise

I. S. Borisov, A. A. Bystrov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (2855 kB) Citations (5)
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DOI: https://doi.org/10.4213/tvp158
Abstract: In this paper the construction of a stochastic integral of a nonrandom function is suggested without the classical orthogonality condition of the noise. This construction includes some known constructions of univariate and multiple stochastic integrals. Conditions providing the existence of this integral are specified for noises generated by random processes with nonorthogonal increments from certain classes which are rich enough.
Keywords: stochastic integral, multiple stochastic integral, noise, Gaussian processes, regular fractional Brownian motion.
Received: 09.06.2004
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 1, Pages 53–74
DOI: https://doi.org/10.1137/S0040585X97981469
Bibliographic databases:
Language: Russian
Citation: I. S. Borisov, A. A. Bystrov, “Constructing a stochastic integral of a nonrandom function without orthogonality of the noise”, Teor. Veroyatnost. i Primenen., 50:1 (2005), 52–80; Theory Probab. Appl., 50:1 (2006), 53–74
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v50/i1/p52
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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