多元正規(guī)變化及其應用.pdf

1、南京師范大學碩士學位論文多元正規(guī)變化及其應用姓名：錢小仕申請學位級別：碩士專業(yè)：數學；運籌學與控制論指導教師：王曉謙2009-04-26南京師范大學碩士學位論文AbstractIn this dissertation multivariate regular variation and generalized multivari-ate regular variation in Rd are studied, and used to c

2、haracterize the domain ofattraction of multivariate extreme value distribution. The main results are asfollows:In chapter 2, weak multivariate regular variation are defi ned. Under thisdefi nition, a analytic expression

3、of the limit function are fi gure out. For weakmultivariate regular variation, uniform convergence theorem, representationtheorem and Potter bounded inequality is also existed. In addition, general-ized regular variation

4、 functions in multidimensional real valued vector spaceare studied and some equivalent conditions are proved.In chapter 3, various defi nitions of multivariate regular variation randomvector are settled and equivalence a

5、mong these defi nitions are proved.In chapter 4, the relations between multivariate regular variation and thedomain of attraction of multivariate extreme value distribution are discussed.Key Words: Regular Variation, Gen