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Volume 62 >>> № 3 MAY — JUNE 2026

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UDC 519.21

A.V. Nikitin
National University "Ostroh Academy," Ostrog, Ukraine,
anatolii.nikitin@oa.edu.ua; Jan Kochanowski University, Kielce,
Poland, anatolii.nikitin@ujk.edu.pl

U.T. Khimka
Ivan Franko National University of Lviv, Lviv, Ukraine,
ulyana.khimka@lnu.edu.ua

S.A. Nechyporuk
National University "Ostroh Academy," Ostrog, Ukraine,
serhii.a.nechyporuk@oa.edu.ua

ESTIMATION OF PARAMETERS OF A TWO-THRESHOLD LEVY PROCESS
BY APPROXIMATE MAXIMUM LIKELIHOOD METHOD

Abstract. Based on the Ito–Skorokhod stochastic differential equation, a construction of a model of a two-threshold process and an approximate maximum likelihood method are proposed, which is based on the approximation of the logarithmic likelihood function of observations. Estimates of the parameters of a three-mode threshold jump process with discretely selected data are found. The model presented in the work takes into account three components: shift, diffusion, and jumps, which make it possible to evaluate both moderate and sharp changes in the behavior of the process. The process is divided into three modes, and the parameters are estimated for each of these ranges. This solution allows analyzing both simple and complex processes with hierarchical dynamics. The developed algorithm is based on an approximate maximum likelihood estimate. The algorithm is built in the format of an iterative procedure, which at each step enumerates the parameters, taking into account the current value of the thresholds. The calculation continues until convergence is achieved.

Keywords: approximate maximum likelihood method, two-threshold Levy process, stochastic differential equation.

full text

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UDC 519.21

ESTIMATION OF PARAMETERS OF A TWO-THRESHOLD LEVY PROCESS BY APPROXIMATE MAXIMUM LIKELIHOOD METHOD

REFERENCES

ESTIMATION OF PARAMETERS OF A TWO-THRESHOLD LEVY PROCESS
BY APPROXIMATE MAXIMUM LIKELIHOOD METHOD