Geodesic
Constructing a stochastic integral of a nonrandom function without orthogonality of the noise
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 1, pp. 52-80

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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, Gaussian processes, regular fractional Brownian motion.
Mots-clés : noise 
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     title = {Constructing a stochastic integral of a nonrandom function without orthogonality of the noise},
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I. S. Borisov; A. A. Bystrov. Constructing a stochastic integral of a nonrandom function without orthogonality of the noise. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 1, pp. 52-80. http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a2/