多元正規(guī)變化及其應(yīng)用.pdf

1、南京師范大學(xué)碩士學(xué)位論文多元正規(guī)變化及其應(yīng)用姓名：錢小仕申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：數(shù)學(xué)；運(yùn)籌學(xué)與控制論指導(dǎo)教師：王曉謙2009-04-26南京師范大學(xué)碩士學(xué)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