Stationarity of Stochastic Linear Equations with Additive Noise and Delays in the Unbounded Drift Terms

Kai Liu

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arXiv · 1402.2199

Stationarity of Stochastic Linear Equations with Additive Noise and Delays in the Unbounded Drift Terms

Kai Liu

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Abstract

This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a consequence, the associated stochastic equations have unbounded operators acting on the discrete or distributed delayed terms, while the operator acting on the instantaneous term generates a strongly continuous semigroup. We present conditions on the delay systems to obtain a unique stationary solution by combining spectrum analysis of unbounded operators and stochastic calculus. A few instructive cases are analyzed in detail to clarify the underlying complexity in the study of systems with unbounded delayed operators.

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BibTeX RIS

Kai Liu. 2014-02-10. Stationarity of Stochastic Linear Equations with Additive Noise and Delays in the Unbounded Drift Terms. https://arxiv.org/abs/1402.2199

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