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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 2005 Volume 50, Issue 1, Pages 52–80 (Mi tvp158)

This article is cited 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

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

DOI: 10.4213/tvp158


 English version:
Theory of Probability and its Applications, 2006, 50:1, 53–74

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