Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear Expectations
Let X,Xn,n≥1 be a sequence of independent, identically distributed random variables under sublinear expectations with CVX2<∞, limc⟶∞EX2−c+=0, and E˘X=E˘−X=0. Write S0=0, Sn=∑k=1nXn, and Mn=max0≤k≤nSk, n≥1. For d>0 and an=olog logn−d, we obtain the exact rates in the law of iterated logarithm o...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2022/7566141 |
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| author | Mingzhou Xu Kun Cheng |
| author_facet | Mingzhou Xu Kun Cheng |
| author_sort | Mingzhou Xu |
| collection | DOAJ |
| description | Let X,Xn,n≥1 be a sequence of independent, identically distributed random variables under sublinear expectations with CVX2<∞, limc⟶∞EX2−c+=0, and E˘X=E˘−X=0. Write S0=0, Sn=∑k=1nXn, and Mn=max0≤k≤nSk, n≥1. For d>0 and an=olog logn−d, we obtain the exact rates in the law of iterated logarithm of a kind of weighted infinite series of CVMn−ε+anσ¯nlog lognd+ as ε↓0. |
| format | Article |
| id | doaj-art-aac7279c5c094305a30805bf757e67a1 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-aac7279c5c094305a30805bf757e67a12025-02-03T01:19:59ZengWileyDiscrete Dynamics in Nature and Society1607-887X2022-01-01202210.1155/2022/7566141Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear ExpectationsMingzhou Xu0Kun Cheng1School of Information EngineeringSchool of Information EngineeringLet X,Xn,n≥1 be a sequence of independent, identically distributed random variables under sublinear expectations with CVX2<∞, limc⟶∞EX2−c+=0, and E˘X=E˘−X=0. Write S0=0, Sn=∑k=1nXn, and Mn=max0≤k≤nSk, n≥1. For d>0 and an=olog logn−d, we obtain the exact rates in the law of iterated logarithm of a kind of weighted infinite series of CVMn−ε+anσ¯nlog lognd+ as ε↓0.http://dx.doi.org/10.1155/2022/7566141 |
| spellingShingle | Mingzhou Xu Kun Cheng Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear Expectations Discrete Dynamics in Nature and Society |
| title | Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear Expectations |
| title_full | Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear Expectations |
| title_fullStr | Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear Expectations |
| title_full_unstemmed | Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear Expectations |
| title_short | Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear Expectations |
| title_sort | note on precise rates in the law of iterated logarithm for the moment convergence of i i d random variables under sublinear expectations |
| url | http://dx.doi.org/10.1155/2022/7566141 |
| work_keys_str_mv | AT mingzhouxu noteonpreciseratesinthelawofiteratedlogarithmforthemomentconvergenceofiidrandomvariablesundersublinearexpectations AT kuncheng noteonpreciseratesinthelawofiteratedlogarithmforthemomentconvergenceofiidrandomvariablesundersublinearexpectations |