000			03547nam a22004455i 4500
001			978-3-540-26312-8
003			DE-He213
005			20161121230931.0
007			cr nn 008mamaa
008			100301s2005 gw | s |||| 0|eng d
020			_a9783540263128 _9978-3-540-26312-8
024	7		_a10.1007/b137401 _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		_aSkorokhod, A.V. _eauthor.
245	1	0	_aBasic Principles and Applications of Probability Theory _h[electronic resource] / _cby A.V. Skorokhod ; edited by Yu.V. Prokhorov.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2005.
300			_aV, 282 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPart I. Probability. Basic Notions, Structure, Methods: Introduction; The Probability Space; Independence; General Theory of Stochastic Processes and Random Functions; Limit Theorems -- Part II. Markov Processes and Probability Applications in Analysis: Markov Processes; Probabilistic Representations of Solutions of Partial Differential Equations; Wiener Process and the Solution of Equations Involving the Laplace Operator -- Part III. Practical Probability Applications: Statistical Methods; Controlled Stochastic Processes; Information; Filtering.
520			_aProbability theory arose originally in connection with games of chance and then for a long time it was used primarily to investigate the credibility of testimony of witnesses in the “ethical” sciences. Nevertheless, probability has become a very powerful mathematical tool in understanding those aspects of the world that cannot be described by deterministic laws. Probability has succeeded in ?nding strict determinate relationships where chance seemed to reign and so terming them “laws of chance” combining such contrasting - tions in the nomenclature appears to be quite justi?ed. This introductory chapter discusses such notions as determinism, chaos and randomness, p- dictibility and unpredictibility, some initial approaches to formalizing r- domness and it surveys certain problems that can be solved by probability theory. This will perhaps give one an idea to what extent the theory can - swer questions arising in speci?c random occurrences and the character of the answers provided by the theory. 1. 1 The Nature of Randomness The phrase “by chance” has no single meaning in ordinary language. For instance, it may mean unpremeditated, nonobligatory, unexpected, and so on. Its opposite sense is simpler: “not by chance” signi?es obliged to or bound to (happen). In philosophy, necessity counteracts randomness. Necessity signi?es conforming to law – it can be expressed by an exact law. The basic laws of mechanics, physics and astronomy can be formulated in terms of precise quantitativerelationswhichmustholdwithironcladnecessity.
650		0	_aMathematics.
650		0	_aProbabilities.
650	1	4	_aMathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
700	1		_aProkhorov, Yu.V. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540546863
856	4	0	_uhttp://dx.doi.org/10.1007/b137401
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c506096 _d506096