partial adj. 1.一部分的,局部的,不完全的。 2.不公平的;偏袒的。 3.偏愛的,特別歡喜的 (to)。 4.【植物;植物學(xué)】后生的,再生的。 partial drought 小旱。 partial in one's judgement 判斷不公平的。 be partial to 偏愛 (He is too partial to tobacco. 他太歡喜抽煙了)。 adv. -ly n. -ness =partiality.
The paper consists of two chapters . in the first chapter , theory 1 [ 1 ] mainly by using the method of the law of the iterated logarithm with finite partial sum in wiener process proves hartman - wintner [ 1 ] law of the iterated logarithm for special finite partial weight sums 本文正文分兩部分,定理1主要利用[ 1 ] wiener過程下的有限項部分和的重對數(shù)律,把hartman - wintner重對數(shù)律[ 1 ]推廣到對特殊加權(quán)部分和也成立。
The limit theory of law of the iterated logarithm have received more and more attentions , especially about identical independent random variables . but up to now , the studies are only for partial sums and , have n ' t shown any concern on the special finite partial weight suras . however , the partial sums and partial weight sums not only have the osculating aspects , but also have essential difference between them . so the studies for these play an important role in theoretical and applied setups 因此對重對數(shù)律的研究引起了國內(nèi)外學(xué)者的興趣,對獨立同分布的隨機變量,許多學(xué)者做了大量的研究工作,但迄今為止這方面的研究仍限于部分和數(shù)列的重對數(shù)律,很少涉及到特殊加權(quán)和的領(lǐng)域,而部分和與加權(quán)和之間既有密切聯(lián)系,又有本質(zhì)不同,因此,這一問題的研究具有一定理論意義和應(yīng)用價值。
Let { xn ; n > 1 } be mutually identically independent random variables distributed according to the normal distribution , { sn , n > 1 } be finite partial sum series , the purpose of this paper is to investigate law of the iterated logarithm type results for special finite partial weight sum series { sn , n > 1 } , we assume that sn = a1sn + a2 ( s2n - sn ) + a3 ( s3n - s2n ) + . . . + ad ( sdn - s ( d - 1 ) n ) in the second chapter , theory 2 by using the method of literature [ 8 ] , we extend hartman - wintner law of iterated logarithm on the gauss distribution . we substitute negative correspond for independent . it extends the corresponding results in gauss distribution 設(shè){ x _ n ; n 1 }是獨立同分布的且服從標(biāo)準(zhǔn)正態(tài)分布的隨機變量序列, { s _ n , n 1 }是其部分和數(shù)列,討論有限項特殊加權(quán)部分和{ s _ n , n 1 }的重對數(shù)律,其中定理2利用文獻(xiàn)[ 8 ]提供的方法,在高斯分布上改進了hartman - wintner的重對數(shù)律,取消獨立性用更弱的條件負(fù)相關(guān)代替,大大拓寬了重對數(shù)律在高斯分布中的使用范圍。