Asymptotic expansion in the zones of large deviations in terms of Lyapunov's fractions
Tarkime, kad atsitiktiniai dyžiai (at.d.) ξj su vidurkiais Eξj = 0 ir dispersijomis σj2 = E ξj2 > 0, j = 1, 2, ... , n, tenkina sąlygą: ∃ dydžiai γ > 0 ir τn > 0 tokie, kad Liapunovo trupmenos Lk, n := ∑j =1n E|ξj|k/ Bnk ≤ (k!)1 + γ/ τnk-2, k =3, 4, ... , Bn2 = ∑j =1n σj2. Esant patenk...
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| Language: | English |
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Vilnius University Press
1998-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://ojs.test/index.php/LMR/article/view/37990 |
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| author | Leonas Saulis |
| author_facet | Leonas Saulis |
| author_sort | Leonas Saulis |
| collection | DOAJ |
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Tarkime, kad atsitiktiniai dyžiai (at.d.) ξj su vidurkiais Eξj = 0 ir dispersijomis σj2 = E ξj2 > 0, j = 1, 2, ... , n, tenkina sąlygą: ∃ dydžiai γ > 0 ir τn > 0 tokie, kad Liapunovo trupmenos Lk, n := ∑j =1n E|ξj|k/ Bnk ≤ (k!)1 + γ/ τnk-2, k =3, 4, ... , Bn2 = ∑j =1n σj2.
Esant patenkintai sąlygai (L*) ir reikalaujant at. d. ξj tankio funkcijos aprėžtumo, darbe gauti P(Zn ≥ x), Zn = Sn/Bn, Sn = ξ1 + ξ2 + ... + ξn asimptotiniai skleidimai didžiųjų nuokrypių zonose 0 ≤ x < τn*, kur τn* = {c τn / |ln τn|, γ = 0, cγ* τn 1/(1 + 2 γ), γ = 0.
x=0,
. x>o.
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| format | Article |
| id | doaj-art-c738593df0dc43f4bd9404c2dbe387df |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 1998-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-c738593df0dc43f4bd9404c2dbe387df2025-01-03T06:37:44ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X1998-12-0138II10.15388/LMD.1998.37990Asymptotic expansion in the zones of large deviations in terms of Lyapunov's fractionsLeonas Saulis0Vilnius Gediminas Technical University Tarkime, kad atsitiktiniai dyžiai (at.d.) ξj su vidurkiais Eξj = 0 ir dispersijomis σj2 = E ξj2 > 0, j = 1, 2, ... , n, tenkina sąlygą: ∃ dydžiai γ > 0 ir τn > 0 tokie, kad Liapunovo trupmenos Lk, n := ∑j =1n E|ξj|k/ Bnk ≤ (k!)1 + γ/ τnk-2, k =3, 4, ... , Bn2 = ∑j =1n σj2. Esant patenkintai sąlygai (L*) ir reikalaujant at. d. ξj tankio funkcijos aprėžtumo, darbe gauti P(Zn ≥ x), Zn = Sn/Bn, Sn = ξ1 + ξ2 + ... + ξn asimptotiniai skleidimai didžiųjų nuokrypių zonose 0 ≤ x < τn*, kur τn* = {c τn / |ln τn|, γ = 0, cγ* τn 1/(1 + 2 γ), γ = 0. x=0, . x>o. https://ojs.test/index.php/LMR/article/view/37990 |
| spellingShingle | Leonas Saulis Asymptotic expansion in the zones of large deviations in terms of Lyapunov's fractions Lietuvos Matematikos Rinkinys |
| title | Asymptotic expansion in the zones of large deviations in terms of Lyapunov's fractions |
| title_full | Asymptotic expansion in the zones of large deviations in terms of Lyapunov's fractions |
| title_fullStr | Asymptotic expansion in the zones of large deviations in terms of Lyapunov's fractions |
| title_full_unstemmed | Asymptotic expansion in the zones of large deviations in terms of Lyapunov's fractions |
| title_short | Asymptotic expansion in the zones of large deviations in terms of Lyapunov's fractions |
| title_sort | asymptotic expansion in the zones of large deviations in terms of lyapunov s fractions |
| url | https://ojs.test/index.php/LMR/article/view/37990 |
| work_keys_str_mv | AT leonassaulis asymptoticexpansioninthezonesoflargedeviationsintermsoflyapunovsfractions |