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Some properties of random fields related to stochastic integrals with respect to strong martingales

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Abstract

We investigate the properties of random fields related to stochastic intergals with respect to a two-parameter strong square-integrable martingale in the case where the martingale and the integrands depend on the limits of integration. We prove inequalities for the moments of the uniform norm and the modulus of continuity of trajectories of modifications of such fields. Bibliography: 8 titles.

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Authors and Affiliations

  1. Volgograd State University, Volgograd, Russia

    N. A. Kolodii

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  1. N. A. Kolodii
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 80–96.

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Kolodii, N.A. Some properties of random fields related to stochastic integrals with respect to strong martingales. J Math Sci 137, 4531–4540 (2006). https://doi.org/10.1007/s10958-006-0246-z

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  • DOI: https://doi.org/10.1007/s10958-006-0246-z

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