000			03676nam a22005055i 4500
001			978-3-540-78859-1
003			DE-He213
005			20161121231215.0
007			cr nn 008mamaa
008			100301s2008 gw | s |||| 0|eng d
020			_a9783540788591 _9978-3-540-78859-1
024	7		_a10.1007/978-3-540-78859-1 _2doi
050		4	_aQA273.A1-274.9
050		4	_aQA274-274.9
072		7	_aPBT _2bicssc
072		7	_aPBWL _2bicssc
072		7	_aMAT029000 _2bisacsh
082	0	4	_a519.2 _223
100	1		_aSchneider, Rolf. _eauthor.
245	1	0	_aStochastic and Integral Geometry _h[electronic resource] / _cby Rolf Schneider, Wolfgang Weil.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2008.
300			_aXII, 694 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProbability and Its Applications, _x1431-7028
505	0		_aFoundations of Stochastic Geometry -- Prolog -- Random Closed Sets -- Point Processes -- Geometric Models -- Integral Geometry -- Averaging with Invariant Measures -- Extended Concepts of Integral Geometry -- Integral Geometric Transformations -- Selected Topics from Stochastic Geometry -- Some Geometric Probability Problems -- Mean Values for Random Sets -- Random Mosaics -- Non-stationary Models -- Facts from General Topology -- Invariant Measures -- Facts from Convex Geometry.
520			_aStochastic geometry has in recent years experienced considerable progress, both in its applications to other sciences and engineering, and in its theoretical foundations and mathematical expansion. This book, by two eminent specialists of the subject, provides a solid mathematical treatment of the basic models of stochastic geometry -- random sets, point processes of geometric objects (particles, flats), and random mosaics. It develops, in a measure-theoretic setting, the integral geometry for the motion and the translation group, as needed for the investigation of these models under the usual invariance assumptions. A characteristic of the book is the interplay between stochastic and geometric arguments, leading to various major results. Its main theme, once the foundations have been laid, is the quantitative investigation of the basic models. This comprises the introduction of suitable parameters, in the form of functional densities, relations between them, and approaches to their estimation. Much additional information on stochastic geometry is collected in the section notes. As a combination of probability theory and geometry, the volume is intended for readers from either field. Probabilists with interest in random spatial structures, or motivated by the prospect of applications, will find an in-depth presentation of the geometric background. Geometers can see integral geometry "at work" and may be surprised to learn how classical results from convex geometry have elegant applications in a stochastic setting.
650		0	_aMathematics.
650		0	_aConvex geometry.
650		0	_aDiscrete geometry.
650		0	_aProbabilities.
650	1	4	_aMathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aConvex and Discrete Geometry.
700	1		_aWeil, Wolfgang. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540788584
830		0	_aProbability and Its Applications, _x1431-7028
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-540-78859-1
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c510137 _d510137