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200 10$aFunctional Equations and Characterization Problems on Locally Compact Abelian Groups$b[electronic resource] /$fGennadiy Feldman
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2008
215   $a1 online resource (268 pages)
225 0 $aEMS Tracts in Mathematics (ETM)$v5
330   $aThis book deals with the characterization of probability distributions. It is well  known that both the sum and the difference of two Gaussian independent  random variables with equal variance are independent as well. The converse statement was  proved independently by M. Kac and S. N. Bernstein. This result is a famous  example of a characterization theorem. In general, characterization problems  in mathematical statistics are statements in which the description of possible  distributions of random variables follows from properties of some functions in  these variables.      In recent years, a great deal of attention has been focused upon generalizing  the classical characterization theorems to random variables with values in  various algebraic structures such as locally compact Abelian groups, Lie  groups, quantum groups, or symmetric spaces. The present book is aimed at  the generalization of some well-known characterization theorems to the case  of independent random variables taking values in a locally compact Abelian  group X. The main attention is paid to the characterization of the Gaussian  and the idempotent distribution (group analogs of the Kac-Bernstein,  Skitovich-Darmois, and Heyde theorems). The solution of the corresponding  problems is reduced to the solution of some functional equations in the  class of continuous positive definite functions defined on the character group  of X. Group analogs of the Crame?r and Marcinkiewicz theorems are also  studied.      The author is an expert in algebraic probability theory. His comprehensive  and self-contained monograph is addressed to mathematicians working in  probability theory on algebraic structures, abstract harmonic analysis,  and functional equations. The book concludes with comments and unsolved  problems that provide further stimulation for future research in the theory.
606   $aProbability & statistics$2bicssc
606   $aProbability theory and stochastic processes$2msc
606   $aAbstract harmonic analysis$2msc
606   $aStatistics$2msc
615 07$aProbability & statistics
615 07$aProbability theory and stochastic processes
615 07$aAbstract harmonic analysis
615 07$aStatistics
686   $a60-xx$a43-xx$a62-xx$2msc
700   $aFeldman$b Gennadiy$01071623
801  0$bch0018173
906   $aBOOK
912   $a9910151935103321
996   $aFunctional Equations and Characterization Problems on Locally Compact Abelian Groups$92567867
997   $aUNINA