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Asymptotic equivalence of linear stochastic Itô systems and oscillation of solutions of linear second-order equations

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Abstract

We obtain conditions for the asymptotic equivalence of linear stochastic and deterministic systems and analyze the oscillation of solutions of the Itô stochastic equation of the second order of the form \(\ddot x + (p(t) + q(t)\dot W(t))x = 0\) on the half-line.

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Authors and Affiliations

  1. Kiev National University, Kiev, Ukraine

    A. N. Stanzhitskii, A. P. Krenevich & I. G. Novak

Authors
  1. A. N. Stanzhitskii
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  2. A. P. Krenevich
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  3. I. G. Novak
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Original Russian Text © A.N. Stanzhitskii, A.P. Krenevich, I.G. Novak, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 6, pp. 796–810.

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Stanzhitskii, A.N., Krenevich, A.P. & Novak, I.G. Asymptotic equivalence of linear stochastic Itô systems and oscillation of solutions of linear second-order equations. Diff Equat 47, 799–813 (2011). https://doi.org/10.1134/S001226611106005X

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  • DOI: https://doi.org/10.1134/S001226611106005X

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