Stochastic Helmholtz Problem and Convergence in Distribution

Tleubergenov M. Vassilina G. Azhymbaev D.
2022 University of Nis

Filomat
2022 #36 Issue 7 2451 - 2460 pp.

In the present paper, the solvability of the stochastic Helmholtz problem is investigated in the class of stochastic differential equations equivalent in distribution. Earlier, by additional variables method the Helmholtz problem was investigated in the class of stochastic differential equations equivalent almost surely (a.s.). The study of the stochastic Helmholtz problem in the class of equations equivalent in distribution allows us to significantly expand the region of its solvability. This is due to the possibility of using well-known methods of the theory of stochastic processes, such as the method of the phase space transformation, the method of absolutely continuous change of measure, and the method of random change of time. In that paper stochastic equations of the Lagrangian structure equivalent in distribution are constructed by the given second order Ito stochastic equations using the methods of phase space transformation, absolutely continuous measure transformation and random time substitution. The obtained results are illustrated by specific examples.

convergence in distribution , Helmholtz inverse problem , Ito stochastic equations

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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Almaty University of Power Engineering and Telecommunications named after G.Daukeev, Almaty, Kazakhstan
K.Zhubanov Aktobe Regional University, Aktobe, Kazakhstan

Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
Almaty University of Power Engineering and Telecommunications named after G.Daukeev
K.Zhubanov Aktobe Regional University

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