Rozora, I. V.I. V.Rozora2026-06-302026-06-302018Rozora, I. V. (2018). Convergence rate for the estimation of impulse response function in the space of continuous functions. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(3), 30–36. https://doi.org/10.17721/1812-5409.2018/3.410.17721/1812-5409.2018/3.4https://ir.library.knu.ua/handle/15071834/26327The problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The sphere of applications of these models is very extensive, ranging from signal processing and automatic control to econometrics (errors-in-variables models). In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function. We assume that impulse function is square-integrable. Input signal is supposed to be Gaussian stationary stochastic process with known spectral density. A sample input–output cross-correlogram is taken as an estimator of the response function. An upper bound for the tail of the distribution of the supremum of the estimation error is found that gives a convergence rate of estimator to impulse response function.Key words: impulse response function, linear time-invariant system (LTI), Gaussian process, crosscorrelogram.Pages of the article in the issue: 30 - 36Language of the article: UkrainianenСтаття