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001			77-091109
003			CH-001817-3
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008			091109e20080429sz fot ||| 0|eng d
020			_a9783037195451
024	7	0	_a10.4171/045 _2doi
040			_ach0018173
072		7	_aPBT _2bicssc
084			_a60-xx _a43-xx _a62-xx _2msc
100	1		_aFeldman, Gennadiy, _eauthor.
245	1	0	_aFunctional Equations and Characterization Problems on Locally Compact Abelian Groups _h[electronic resource] / _cGennadiy Feldman
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2008
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2008
300			_a1 online resource (268 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aEMS Tracts in Mathematics (ETM) _v5
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_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 Cramér 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.
650	0	7	_aProbability & statistics _2bicssc
650	0	7	_aProbability theory and stochastic processes _2msc
650	0	7	_aAbstract harmonic analysis _2msc
650	0	7	_aStatistics _2msc
700	1		_aFeldman, Gennadiy, _eauthor.
856	4	0	_uhttps://doi.org/10.4171/045
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/feldman_mini.jpg
942			_2EBK13762 _cEBK
999			_c50386 _d50386