This article is cited in 2 papers

Continual analogues of random polynomials that are orthogonal on a circle

A. V. Teplyaev

Saint-Petersburg, Russia

Abstract: The paper obtains conditions providing absolute continuity almost surely for the spectral measure of the corresponding random differential operators for a class of canonical systems of ordinary differential equations with random coefficients. Estimates for the densities of the spectral measures are given. Corollaries corresponding to the deterministic case are formulated. Systems of stochastic differential equations with similar properties are considered.

Keywords: random ordinary differential operator, spectral measure, absolutely continuous spectrum, Krein's canonical differential system, stochastic differential equation.

Received: 05.03.1991

 English version: Theory of Probability and its Applications, 1994, 39:3, 476–489

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