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The Convolutions of Non-identical Distributions and the Tail Probability for the Supremum of a Random Walk

Author: LiuXiJun
Tutor: WangYueBao
School: Suzhou University
Course: Probability Theory and Mathematical Statistics
Keywords: Convolution ( Convolution root ) Local subexponential Local Closure Local progressive Random Walks Supremum Inequality NUOD
CLC: O211.3
Type: Master's thesis
Year: 2008
Downloads: 17
Quote: 0
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Well known that the distribution theory is one of the foundations of probability theory , and it Random Walks , which have important applications in the field of risk theory, queuing system, branching process people's attention , which has been one of the core issues of distribution theory the so-called convolution ( including convolution root ) closed and progressive the second chapter of the first part of local support different distribution on [ 0 , ∞ ) convolution ( convolution root ) closure and Local progressive sufficient conditions and necessary conditions , so as to reveal the intrinsic relationship between the different distribution convolution and convolution . fully part of the promotion of this result Geluk and De Vries ( 2006 ) non-local the corresponding results , and the use of both methods is the type of Geluk and De Vries ( 2006 ) ; necessity of this result the latter part of the second chapter is discussed ( - ∞ , ∞ ) different distribution of the partial closure of the convolution and local progressive Chapter III of this paper has been a negative dependent increment generated random walk supremum tail probability of a bound inequality results generalize Leipus and ( ? ) iaulys ( 2007 ) generated by the independent increment the corresponding results of the random walk , the two methods used are different . inequality prepared to discuss some negative dependency claims and waiting time ruin probability progressive conditions . Finally, we pointed out that the fact Leipus ( ? ) iaulys ( 2007 ) results is included in the ( A ) Veraverbeke ( 1977 ) Theorem2 .

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Distribution theory
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