Geodesic
Stochastic Helmholtz problem and convergence in distribution
Filomat, Tome 36 (2022) no. 7, p. 2451

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DOI

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.
DOI : 10.2298/FIL2207451T
Classification : 60H10, 34F05, 34A55
Keywords: Ito stochastic equations, Helmholtz inverse problem, convergence in distribution 
Marat Tleubergenov; Gulmira Vassilina; Darkhan Azhymbaev. Stochastic Helmholtz problem and convergence in distribution. Filomat, Tome 36 (2022) no. 7, p. 2451 . doi: 10.2298/FIL2207451T
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     title = {Stochastic {Helmholtz} problem and convergence in distribution},
     journal = {Filomat},
     pages = {2451 },
     year = {2022},
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     doi = {10.2298/FIL2207451T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2207451T/}
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