In this note the author establishes the invarianee principle for ρ-mixing sequences under combinations of moment assumptions and ρ-mixing rates. The result answers a problem from a recent survey paper of Peligrad.
It is well known that there are many authors who have thoroughly investigated the complete convergence for non-random partial sums of i. i. d. random variables, such as Katz and Baum, BAI Zhi-dong and SHU Chun. In [2]...It is well known that there are many authors who have thoroughly investigated the complete convergence for non-random partial sums of i. i. d. random variables, such as Katz and Baum, BAI Zhi-dong and SHU Chun. In [2], BAI and SHU also considered展开更多
Csorgo and Revesz (1981) obtained an elegant result on how ismall the increments ofpartial sums of IID random variables are. But their proof seems some wrong. In this paperwe have not only corrected their proof, but a...Csorgo and Revesz (1981) obtained an elegant result on how ismall the increments ofpartial sums of IID random variables are. But their proof seems some wrong. In this paperwe have not only corrected their proof, but also established the corresponding result forindependent, not necessarily identically distributed random variables under more generaland weaker assumptions.展开更多
Using suitable self-normalization for partial sums of i.i.d.random variables,Griffin and Kuelbs established the law of the iterated logarithm for all distributions in the domain of attraction of a normal law.We obtain...Using suitable self-normalization for partial sums of i.i.d.random variables,Griffin and Kuelbs established the law of the iterated logarithm for all distributions in the domain of attraction of a normal law.We obtain the corresponding results for Studentized increments of partial sums under thesame condition.展开更多
This paper contains the Kolmogorov-Prokhorov exponential inequalities for dependent randomvariables, i.e., for φ-mixing, ρ--mixing and α--mixing. As an application, the law of iteratedlogarithm is established for s...This paper contains the Kolmogorov-Prokhorov exponential inequalities for dependent randomvariables, i.e., for φ-mixing, ρ--mixing and α--mixing. As an application, the law of iteratedlogarithm is established for stationary α--mixing sequence under a nearly best assumption.展开更多
文摘In this note the author establishes the invarianee principle for ρ-mixing sequences under combinations of moment assumptions and ρ-mixing rates. The result answers a problem from a recent survey paper of Peligrad.
基金Project supported by the National Natural Science Foundation of China.
文摘It is well known that there are many authors who have thoroughly investigated the complete convergence for non-random partial sums of i. i. d. random variables, such as Katz and Baum, BAI Zhi-dong and SHU Chun. In [2], BAI and SHU also considered
基金Project supported by the Fok Yingtung Education Foundation,and by the National Natural Science Foundation of China.
文摘Csorgo and Revesz (1981) obtained an elegant result on how ismall the increments ofpartial sums of IID random variables are. But their proof seems some wrong. In this paperwe have not only corrected their proof, but also established the corresponding result forindependent, not necessarily identically distributed random variables under more generaland weaker assumptions.
基金Project supported by the National Natural Science Foundation of Chinaan NSERC Canada grant of M.Csorgo at Carletoa University of Canada+1 种基金the Fok Yingtung Education Foundationan NSERC Canada Scientific Exchange Award at Carleton University
文摘Using suitable self-normalization for partial sums of i.i.d.random variables,Griffin and Kuelbs established the law of the iterated logarithm for all distributions in the domain of attraction of a normal law.We obtain the corresponding results for Studentized increments of partial sums under thesame condition.
基金Research supported by National Science Foundation Grant
文摘This paper contains the Kolmogorov-Prokhorov exponential inequalities for dependent randomvariables, i.e., for φ-mixing, ρ--mixing and α--mixing. As an application, the law of iteratedlogarithm is established for stationary α--mixing sequence under a nearly best assumption.
