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Order reduction for a system of stochastic differential equations with a small parameter in the coefficient of the leading derivative. Estimate for the rate of convergence

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Abstract

We establish an estimate for the rate of convergence of a solution of an ordinary stochastic differential equation of order p ≥ 2 with a small parameter in the coefficient of the leading derivative to a solution of a stochastic equation of order p − 1 in the metric ρ(X, Y) = (sup0≤t≤T M|X(t) − Y(t)|2)1/2

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Authors and Affiliations

  1. Donetsk National University, Donetsk

    B. V. Bondarev & E. E. Kovtun

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  1. B. V. Bondarev
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  2. E. E. Kovtun
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1587–1601, December, 2006.

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Bondarev, B.V., Kovtun, E.E. Order reduction for a system of stochastic differential equations with a small parameter in the coefficient of the leading derivative. Estimate for the rate of convergence. Ukr Math J 58, 1799–1817 (2006). https://doi.org/10.1007/s11253-006-0169-3

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  • DOI: https://doi.org/10.1007/s11253-006-0169-3

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