【作者】 刘希军；

【导师】 王岳宝；

【作者基本信息】 苏州大学 ， 概率论与数理统计， 2008， 硕士

【摘要】 周知,分布理论是概率论的基础之一,而且它在随机游动,从而在风险理论,排队系统,分支过程等领域有重要的应用,因而一直受到人们的关注.分布理论的核心问题之一是所谓的卷积(包括卷积根)的封闭性及渐进性.本文第二章的前一部分分别得到了支撑在[O,∞)上的不同分布的卷积(包括卷积根)的局部封闭性及局部渐进性的充分条件和必要条件,从而揭示了不同分布的卷积及两两卷积之间的内在关系.这一结果的充分性部分推广了Geluk及De Vries(2006)非局部的相应结果,并且两者使用的方法是不同的;而这一结果的必要性部分是Geluk及De Vries(2006)所没有的.第二章的后一部分,讨论了(-∞,∞)上不同分布卷积的局部封闭性及局部渐进性.本文第三章得到了一类负相依增量生成的随机游动上确界的尾概率的一个上界不等式.这一结果推广了Leipus及(?)iaulys(2007)由独立增量生成的随机游动的相应结果,两者使用的方法也是不同的.这一不等式为讨论一些负相依索赔和等待时间的破产概率的渐进性准备了条件.最后,我们指出,Leipus及(?)iaulys(2007)的结果事实上已包含在Veraverbeke(1977)的Theorem2(A)中.更多还原

【Abstract】 It is well known that the distribution theory is one foundations of probability,and it have very important applications in random walk,and so in risk theory,queueing theory,branching process theory and so on.So they have been paid wide attentions. While one key problem of the distribution theory is so called the closure and asymptotic of convolution,including the convolution roots.In the first part of the second chapter,we obtain sufficient conditions and necessary conditions of local closure and local asymptotics for the convolutions(including convolution roots)of non-identical distributions on[0,∞),which reveal the relations between convolutions and pairwise convolutions of non-identical distributions.The sufficient part of the result extends the corresponding,non-local result of Geluk and De Vries(2006),and the methods we use are different from theirs;whatever,the necessary part of the result is not included in Geluk and De Vries(2006).In the last part of the second chapter,we discuss the local closure and local asymptotics for the convolutions of non-identical distributions on (-∞,∞).In the third chapter,we obtain an upper bound inequality of tail probability for the supremum of a random walk that is formed by a class of negative associated increments.The result extends the corresponding result of Leipus and(?)iaulys(2007) which is formed by a class of independent increments and the method we Use is different from their.The inequality prepaires for discssing the asymptotic of rum probability for some negative associated claims and waited time.Finally,we point out that the result of(?)iaulys(2007),in fact,is included by Theorem2(A)of Veraverbeke(1977)更多还原