000			03911nam a22003978i 4500
001			CR9780511721397
003			UkCbUP
005			20200124160232.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100303s2008||||enk o ||1 0|eng|d
020			_a9780511721397 (ebook)
020			_z9780521881173 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
041	1		_aeng _hrus
050	0	0	_aQA274.73 _b.B67 2008
082	0	4	_a519.282 _222
100	1		_aBorovkov, A. A. _q(Aleksandr Alekseevich), _d1931- _eauthor.
245	1	0	_aAsymptotic analysis of random walks : _bheavy-tailed distributions / _cA.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova.
264		1	_aCambridge : _bCambridge University Press, _c2008.
300			_a1 online resource (xxix, 625 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _vvolume 118
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aPreliminaries -- Random walks with jumps having no finite first moment -- Random walks with jumps having finite mean and infinite variance -- Random walks with jumps having finite variance -- Random walks with semiexponential jump distributions -- Large deviations on the boundary of and outside the Cramer zone for random walks with jump distributions decaying exponentially fast -- Asymptotic properties of functions of regularly varying and semiexponential distributions. Asymptotics of the distributions of stopped sums and their maxima. An alternative approach to studying the asymptotics of P(S[subscript n] [is equal to or greater than] x) -- On the asymptotics of the first hitting times -- Integro-local and integral large deviation theorems for sums of random vectors -- Large deviations in trajectory space -- Large deviations of sums of random variables of two types -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances -- Random walks with dependent jumps -- Extension of the results of Chapters 2-5 to continuous-time random processes with independent increments -- Extension of the results of Chapters 3 and 4 to generalized renewal processes.
520			_aThis book focuses on the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors.
650		0	_aRandom walks (Mathematics)
650		0	_aAsymptotic expansions.
700	1		_aBorovkov, K. A. _q(Konstantin Aleksandrovich), _eeditor.
700	1		_aBorovkova, O. B., _etranslator.
776	0	8	_iPrint version: _z9780521881173
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 118.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511721397
999			_c517728 _d517726