2017
Том 69
№ 7

All Issues

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

Krenevych A. P., Stanzhitskii A. N.

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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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 4, pp 619-629.

Citation Example: Krenevych A. P., Stanzhitskii A. N. Investigation of exponential dichotomy of linear Itô stochastic systems with random initial data by using quadratic forms // Ukr. Mat. Zh. - 2006. - 58, № 4. - pp. 543–553.

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