Abstract
We consider one class of Gaussian random processes that are not semimartingales but their increments can play the role of a random measure. For an extended stochastic integral with respect to the processes considered, we obtain the Itô formula.
Similar content being viewed by others
References
A. V. Skorokhod, “On one generalization of a stochastic integral,” Teor. Ver. Primen., 20, No. 2, 223–237 (1975).
T. Sekiguchi and Y. Shiota, “L2-theory of non-causal stochastic integrals,” Math. Repts. Toyama Univ., 8, 119–195 (1985).
E. Pardoux and D. Nualart, “Stochastic calculus with anticipating integrands,” Probab. Theory Related Fields, 78, 535–581 (1988).
Yu. L. Daletskii, “A biorthogonal analog of Hermite polynomials and inversion of the Fourier transformation with respect to a non-Gaussian measure,” Funkts. Anal. Prilozhen., 25, No. 2, 68–70 (1991).
A. A. Dorogovtsev, Stochastic Equations with Anticipation [in Russian], Institute of Mathematics of the Ukrainian Academy of Sciences, Kiev (1996).
M. Sh. Birman and M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in a Hilbert Space [in Russian], Leningrad University, Leningrad (1980).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 4, pp. 485–495, April, 1998.
Rights and permissions
About this article
Cite this article
Dorogovtsev, A.A. Stochastic integration and one class of Gaussian random processes. Ukr Math J 50, 550–561 (1998). https://doi.org/10.1007/BF02487387
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487387