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Investigation of exponential dichotomy of linear Itô stochastic systems with random initial data by using quadratic forms

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Abstract

We study conditions for the mean-square exponential dichotomy of linear Itô stochastic systems. We prove that a sufficient condition for exponential dichotomy is the existence of a quadratic form whose derivative along the solutions of a system is negative definite. The converse theorem is also proved.

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Authors and Affiliations

  1. Shevchenko Kyiv National University, Kyiv

    O. M. Stanzhyts’kyi & A. P. Krenevych

Authors
  1. O. M. Stanzhyts’kyi
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  2. A. P. Krenevych
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 543–553, April, 2006.

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Stanzhyts’kyi, O.M., Krenevych, A.P. Investigation of exponential dichotomy of linear Itô stochastic systems with random initial data by using quadratic forms. Ukr Math J 58, 619–629 (2006). https://doi.org/10.1007/s11253-006-0087-4

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  • DOI: https://doi.org/10.1007/s11253-006-0087-4

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