Estimation of an Unknown Parameter in the Cauchy Problem for a First-Order Partial Differential Equation under Small Gaussian Perturbations

• Datum: 2000
• Hauptverfasser: Bondarev, B. V., Dzundza, A. I., Simogin, A. A., Бондарев, Б. В., Дзундза, А. И., Симогин, А. А.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2000
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4502
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

On the basis of observation of a realization of a solution of the Cauchy problem, we establish a maximum-likelihood estimate for an unknown parameter. We construct an exponential inequality for the probabilities of large deviations of the estimate from the real value of the parameter.