Open AccessON LARGE DEVIATIONS FOR THE SOLUTIONS OF STOCHASTIC PROGRAMMING PROBLEMS
Author(s) -
P. S. Knopov,
AUTHOR_ID,
E. J. Kasitskaya,
AUTHOR_ID
Publication year - 2021
Publication title -
žurnal občislûvalʹnoï ta prikladnoï matematiki
Language(s) - English
Resource type - Journals
eISSN - 2706-9699
pISSN - 2706-9680
DOI - 10.17721/2706-9699.2021.2.04
Subject(s) - stationary point , mathematics , stationary sequence , mixing (physics) , random field , lemma (botany) , function (biology) , large deviations theory , consistency (knowledge bases) , stochastic process , rate function , stationary process , mathematical optimization , mathematical analysis , statistical physics , discrete mathematics , ecology , statistics , physics , poaceae , quantum mechanics , evolutionary biology , biology
The work deals with stochastic programming problems for stationary random sequences, stationary processes, homogeneous random fields with discrete and continuous parameters. Trajectories of processes and fields are continuous. Stationary and no stationary observations of processes and fields are considered. The former criterion function is approximated by the empirical one. It is assumed that the first problem has a unique solution. Consistency of empirical estimates for no stationary observations is proved. Borel–Cantelly lemma is used for proving. Processes and fields are assumed to satisfy the strong mixing condition. Some restrictions on the moments of processes and fields must be fulfilled. Large deviations of the solutions are estimated. For proving the results theorems from functional analysis and large deviations theory are used. Additional conditions on behavior of minimizing function in the neighborhood of the minimum point are supposed. No stationary model is considered for the convex criterion function. The processes and fields need to satisfy the first hypothesis of hypermixing.