000			03038nam a2200397 i 4500
001			CR9781009093965
003			UkCbUP
005			20240905181748.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			210517s2022||||enk o ||1 0|eng|d
020			_a9781009093965 (ebook)
020			_z9781009098441 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
041	1		_aeng _hrus
050	0	0	_aQA273.67 _b.B67 2022
082	0	0	_a519.2 _223/eng20220215
100	1		_aBorovkov, A. A. _q(Aleksandr Alekseevich), _d1931- _eauthor.
245	1	0	_aCompound renewal processes / _cA.A. Borovkov ; translated by Alexey Alimov.
264		1	_aCambridge ; New York : _bCambridge University Press, _c2022.
300			_a1 online resource (xvi, 362 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 ; _v184
500			_aTitle from publisher's bibliographic system (viewed on 20 Jun 2022).
505	0		_aMain limit laws in the normal deviation zone -- Integro-local limit theorems in the normal deviation zone -- Large deviation principles for compound renewal processes -- Large deviation principles for trajectories of compound renewal processes -- Integro-local limit theorems under the Cramér moment condition -- Exact asymptotics in boundary crossing problems for compound renewal processes -- Extension of the invariance principle to the zones of moderately large and small deviations -- Appendix. On boundary crossing problems for compound renewal processes when the Cramér condition is not fulfilled.
520			_aCompound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.
650		0	_aLimit theorems (Probability theory)
650		0	_aDeviation (Mathematics)
700	1		_aAlimov, Alexey, _etranslator.
776	0	8	_iPrint version: _z9781009098441
830		0	_aEncyclopedia of mathematics and its applications ; _v184.
856	4	0	_uhttps://doi.org/10.1017/9781009093965
942			_2ddc _cEB
999			_c9619 _d9619