We consider the problem of estimation of density of a random variable playing the role of initial value for a certain dynamics. The dynamics is defined by a differential equation whose solution is observable at the end of an interval. This problem is called the problem of estimation according to indirect observations. We propose a procedure for the estimation of density based on the method of transformation of measure along the integral curve in combination with kernel estimates.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory, Interscience, New York (1958).
É. A. Nadaraya and R. M. Absava, Some Problems of the Theory of Nonparametric Estimation of the Functional Characteristics of the Law of Distribution of Observations [in Russian], Tbilisi University, Tbilisi (2005).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 3, pp. 427–431, March, 2011.
Rights and permissions
About this article
Cite this article
Tkeshelashvili, A.S. On the statistical estimation of the initial probability distribution based on the observations of dynamics at the end of an interval. Ukr Math J 63, 494–499 (2011). https://doi.org/10.1007/s11253-011-0518-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-011-0518-8